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pure-noise 0.1.0.1 → 0.2.2.0

raw patch · 30 files changed

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CHANGELOG.md view
@@ -8,6 +8,120 @@  ## Unreleased +## 0.2.2.0 2026-07-19++This is the final release of the 0.2.2.0 line.++### Added++- Exports for `mkNoise1`, `mkNoise2`, and `mkNoise3`, in case library users+  wish to hoist custom kernels.+- FastNoiseLite comparisons are now in-repository and reproducible. Comparison+  mechanism goes through tasty-bench.+- The sdist now includes `bench/fnl-compare/cbits/FastNoiseLite.h`, so the+  FNL comparison benchmark can build from a Hackage tarball.+- 3D counterparts for the simplex and cellular families: `openSimplex3`,+  `superSimplex3`, and `cellular3`.+- Flag `optimize`, with default `true`, which bumps the library's optimization level+  to `-O2` by default. Refer to the flag's documentation for rationale.+- Flag `mfma`, which will set `-mfma` for GHC, and may open pathways to+  fused-multiply-add optimizations+- Flag `mavx`, which will set `-mavx` for GHC, and may open pathways for AVX2+  SIMD optimization in the future.+- Flag `llvm-bench` (manual, default off) gating all LLVM-specific benchmark+  options (`-fllvm`, pinned `opt`/`llc`/`clang`, `-mavx`, `-mfma`,+  `-optlc-fp-contract=fast`).+- Benchmark runs now write a `.meta` provenance sidecar (toolchain versions,+  CPU governor/turbo state, AC power state, pinning) next to each CSV.++### Changed++- `pure-noise` now builds at `-O2` by default.+- Project now uses haskell.nix instead of Stack.+- Various updates to documentation, to improve quality+- Performance documentation and results tables re-collected on the 0.2.2.0+  toolchain (README.md and bench/README.md).+- `tested-with: GHC == 9.6.7, 9.8.4, 9.12.2`.++### Fixed++- Replace `round`-based rounding with a truncating `fastRound`. This replaces an+  `rintFloat` call in the core lowering with a `float2Int` call, which improves+  performance in hot loops.+  - This changes `cellular2` output at half-integer coordinates: cell selection+    now rounds half away from zero, matching FastNoiseLite's `FastRound`, rather+    than half to even. Numerically observable but visually imperceptible.+- Match FastNoiseLite's evaluation order in `openSimplex2`'s middle-corner+  contribution. Output changes by a few ULP.+- Fix an issue with the 3D benchmark harness where degenerate index math+  collapsed the sample set to ~4 distinct points, providing a poor signal on+  real-world performance.++## 0.2.1.1 2025-10-31++### Changed++- Fixed some errata in the documentation++## 0.2.1.0 2025-10-31++### Added++- 1D noise support with `noise1At` evaluation function+- Noise slicing functions (`sliceX2`, `sliceY2`, `sliceX3`, `sliceY3`, `sliceZ3`) for reducing noise dimensionality+- Comprehensive Haddock documentation for:+  - Core `Noise p v` type with usage examples+  - All utility functions (`warp`, `reseed`, `remap`, `blend`)+  - All slicing functions with examples+- Exported utility functions:+  - `warp` - transform coordinate space+  - `reseed` - modify seed for independent layers (generalizes `alterSeed2`/`alterSeed3`)+  - `remap` - transform noise values (alias for `fmap`)+  - `blend` - combine noise functions with custom blending (alias for `liftA2`)+- Exported `Noise` type for advanced usage and type annotations++### Changed++- Refactored to unified noise representation using `newtype Noise p v`+  - `Noise2` and `Noise3` are now type aliases: `Noise (a,a) a` and `Noise (a,a,a) a`+  - Provides `Functor`, `Applicative`, `Monad`, `Num`, `Fractional`, and `Floating` instances+  - All dimensions share the same instance implementations for consistency+- Updated module documentation with examples of new features (slicing, warping, layering)+- Improved README with advanced usage examples++### Performance++- **Overall**: 90% of benchmarks improved with +32.4% average performance gain+- **Ping-pong fractals**: Branchless optimization yields 110-148% improvement (perlin, value, openSimplex)+- **Cellular noise**: REWRITE RULES for gradient lookups provide 61-70% improvement+- **3D ValueCubic fractals**: Fixed performance regression, achieving 45-80% improvement+- **Perlin noise**: 10-63% improvements from optimized lerp/cubic interpolation with REWRITE RULES+- **Value noise**: 11-43% improvements from interpolation optimizations+- **OpenSimplex2**: 6-16% improvement for Float; minor regression (~5%) for Double variants+- **SuperSimplex2**: Shows 3-21% regression due to improved benchmark methodology+  - Previous benchmarks used same X/Y offset (diagonal sampling), which favored SuperSimplex's triangular lattice+  - New benchmarks use independent X/Y offsets for realistic 2D coordinate distributions+  - Algorithm remains functionally correct; numbers now reflect true 2D performance++## 0.2.0.0 - 2025-10-21++### Added++- Comprehensive haddock documentation for main `Numeric.Noise` module with usage examples++### Changed++- Migrated internal implementation from `vector` to `primitive` (PrimArray)+- Removed `vector` dependency from library (still used in benchmarks)+- Require GHC 9.2+ (base >= 4.16)+- Hide internal modules from public API (`Numeric.Noise.Internal`, `Numeric.Noise.Internal.Math`)+- Improved cellular noise performance by 20-30% through specialized computation paths for different result types++### Fixed++- Fixed intermediate list allocation in fractal functions on GHC 9.6++- Improved division performance for `Noise3` instances+ ## 0.1.0.1 - 2024-10-15  - Add bounds for vector
+ LICENSE_FastNoiseLite view
@@ -0,0 +1,22 @@+MIT License++Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com)+Copyright(c) 2020 Contributors++Permission is hereby granted, free of charge, to any person obtaining a copy+of this software and associated documentation files (the "Software"), to deal+in the Software without restriction, including without limitation the rights+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell+copies of the Software, and to permit persons to whom the Software is+furnished to do so, subject to the following conditions:++The above copyright notice and this permission notice shall be included in all+copies or substantial portions of the Software.++THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE+SOFTWARE.
README.md view
@@ -2,75 +2,269 @@  Performant, modern noise generation for Haskell with a minimal dependency footprint. -The algorithms used in this library are ported from [FastNoiseLite](https://github.com/Auburn/FastNoiseLite). The library structure has been retuned to fit better with Haskell semantics.+## Core features -The public interface for this library is unlikely to change much, although the implementations (`noiseBaseN` functions and anything in `Numeric.Noise.Internal`) are subject to change and may change between minor versions.+- **algebraic composition** of noise functions. You can combine,+  layer, and transform noise sources using standard operators (E.g., `Num`,+  `Fractional`, `Monad`, etc).+- **Complex effects** like domain warping and multi-octave fractals with clean,+  type-safe composition.+- **Competitive with C++**: roughly 70-100% of FastNoiseLite's single-threaded+  random-access throughput under the LLVM backend. And 2D cellular noise runs+  ahead of C++, measured against an optimized FNL build. +**For detailed FastNoiseLite comparison, methodology, and reproducibility instructions,+see the [benchmark README](https://github.com/jtnuttall/pure-noise/blob/main/bench/README.md).**++The public interface for this library is unlikely to change much, although the+implementations (`noiseBaseN` functions and anything in `Numeric.Noise.Internal`)+are subject to change and may change between minor versions.++## Acknowledgments++- This project grew from a port of the excellent+  [FastNoiseLite](https://github.com/Auburn/FastNoiseLite) library. The library+  structure has been tuned to perform well in Haskell and fit well with Haskell+  semantics, but the core noise share their origin with FNL.+- All credit for the original design, algorithms, and implementation goes to its+  creator **[Jordan Peck (@Auburn)](https://github.com/Auburn)**. I'm grateful for+  their work and the opportunity to learn from it.+- The original FastNoiseLite code, from which the core algorithms in this library+  were originally ported, is (C) 2020 Jordan Peck and is licensed under the MIT+  license, a copy of which is included in this repository.++## FastNoiseLite compatibility++pure-noise shares its lineage with FNL, but it isn't intended as a 1:1 port —+kernels are restructured for GHC, and some families intentionally diverge.+Where outputs stand today:++| family                                   | output vs FNL                                 |+| ---------------------------------------- | --------------------------------------------- |+| `perlin2/3`, `cellular2/3`               | bit-exact                                     |+| `openSimplex2/3`, `superSimplex2/3`      | within a few ULP                              |+| `value2/3`, `valueCubic2/3`              | diverges (hash finalization)                  |+| `fractal2/3`, `ridged2/3`, `pingPong2/3` | diverges (octave normalization and weighting) |+| `billow2/3`                              | no FNL counterpart                            |++> [!IMPORTANT]+>+> The `value`, `valueCubic`, and fractal families will align with FNL in 0.3,+> which changes their output for a given seed. Pin `pure-noise < 0.3` if you+> depend on seed-stable output from them.+ ## Usage -The library exports newtypes for N-dimensional noise. Currently, these are just functions that accept a seed and a point in N-dimensional space. They can be arbitrarily unwrapped by with the `noiseNAt` family of functions. Since they abstract over the given seed and parameters, they can be composed with `Num` or `Fractional` methods at will with little-to-no performance cost.+The library provides composable noise functions. `Noise2` and `Noise3` are type+aliases for 2D and 3D noise. Noise functions can be composed transparently using+standard operators with minimal performance cost. -Noise values are generally clamped to `[-1, 1]`, although some noise functions may occasionally produce values slightly outside this range.+Noise values are generally clamped to `[-1, 1]`, although some noise functions+may occasionally produce values slightly outside this range. +### Basic Example+ ```haskell import Numeric.Noise qualified as Noise -myNoise2 :: (RealFrac a) => Seed -> a -> a -> a+-- Compose multiple noise sources+myNoise2 :: (RealFrac a) => Noise.Seed -> a -> a -> a myNoise2 =   let fractalConfig = Noise.defaultFractalConfig-  in Noise.noise2At $-      Noise.fractal2 fractalConfig ((perlin2 + superSimplex2) / 2)+      combined = (Noise.perlin2 + Noise.superSimplex2) / 2+  in Noise.noise2At $ Noise.fractal2 fractalConfig combined ``` +### Advanced Features++The library's unified `Noise p v` type enables powerful composition patterns:++#### Complex Compositions++The `Monad` instance is useful to create noise that depends on other noise values:++```haskell+-- Use one noise function's output to modulate another+complexNoise :: Noise.Noise2 Float+complexNoise = do+  baseNoise <- Noise.perlin2+  detailNoise <- Noise.next2 Noise.superSimplex2+  -- Blend based on base noise: smooth areas get less detail+  pure $ baseNoise * 0.7 + detailNoise * (0.3 * (1 + baseNoise) / 2)+```++This is especially useful for creating organic, varied terrain where one noise pattern+influences the characteristics of another.++#### 1D Noise via Slicing++Generate 1D noise by slicing higher-dimensional noise at a fixed coordinate:++```haskell+-- Create 1D noise by fixing one dimension+noise1d :: Noise.Noise1 Float+noise1d = Noise.sliceY2 0.0 Noise.perlin2++-- Evaluate at a point+value = Noise.noise1At noise1d seed 5.0+```++**Coordinate Transformation:**++Scale, rotate, or warp the coordinate space:++```haskell+-- Double the frequency+scaled = Noise.warp (\(x, y) -> (x * 2, y * 2)) Noise.perlin2++-- Rotate 45 degrees+rotated = Noise.warp (\(x, y) ->+  let a = pi / 4+  in (x * cos a - y * sin a, x * sin a + y * cos a)) Noise.perlin2+```++#### Layering Independent Noise++Use `reseed` or `next2`/`next3` to create independent layers:++```haskell+layered = (Noise.perlin2 + Noise.next2 Noise.perlin2) / 2+```+ More examples can be found in `bench` and `demo`. +#### Domain Warping++Domain warping uses one noise function to distort the coordinate space of another,+creating organic, flowing patterns ideal for terrain, clouds, and natural textures:++```haskell+domainWarped :: Noise.Noise2 Float+domainWarped = do+  -- Generate 3D fractal for warp offsets+  let warpNoise = Noise.fractal3 Noise.defaultFractalConfig{Noise.octaves = 5} Noise.perlin3+  -- Sample 3D noise at different slices to create warp offsets+  warpX <- Noise.sliceX3 0.0 warpNoise  -- Samples at (0, x, y)+  warpY <- Noise.sliceY3 0.0 warpNoise  -- Samples at (x, 0, y)+  -- Apply warping to base noise coordinates+  Noise.warp (\(x, y) -> (x + 30 * warpX, y + 30 * warpY))+    $ Noise.fractal2 Noise.defaultFractalConfig{Noise.octaves = 5} Noise.openSimplex2+```++![Domain Warped Noise](https://raw.githubusercontent.com/jtnuttall/pure-noise/main/demo/images/domain-warp.png)++See the [demo app](demo/) for an interactive version with adjustable parameters.+ ## Performance notes -- This library benefits considerably from compilation with the LLVM backend (`-fllvm`). Benchmarks suggest a ~50-80% difference depending on the kind of noise.+- In single-threaded scenarios with LLVM enabled, this library reaches+  **roughly 70-100% of C++ FastNoiseLite throughput at random access, with 2D+  cellular noise ~7% faster than C++**. Grid-coherent workloads measure lower+  for the simplex family. These numbers are measured against an optimized+  FNL build (AVX2+FMA, FP contraction on).+- This library performs significantly better under the LLVM backend+  (`-fllvm`); the native code generator is not recommended where generation+  speed is a real concern.+- See the [benchmark README](https://github.com/jtnuttall/pure-noise/blob/main/bench/README.md)+  for per-algorithm, per-workload results and methodology. -## Benchmarks+### Recommended build flags -### Results+#### Native optimization flags for the library -Measured by values / second generated by the noise functions. These results come from a benchmark with `-fllvm` enabled.+For the library itself, copy `cabal.project.local.template` into your project+(`+optimize` is on by default; `+mfma +mavx` are safe on modern x86-64). -All results are for `Float`s.+For bulk generation, prefer parallel evaluation via `massiv`. -There's inevitably some noise in the measurements because all of the results are forced into an unboxed vector.+#### Fused multiply add -#### 2D+For the fastest downstream executables, compile the modules that _call_ the+noise functions (the kernels inline into your code) with: -| name          | values / second |-| ------------- | --------------- |-| value2        | 157_347_680     |-| perlin2       | 129_541_747     |-| openSimplex2  | 64_758_006      |-| superSimplex2 | 64_072_639      |-| valueCubic2   | 52_110_819      |-| cellular2     | 15_743_434      |+```+-fllvm -mavx -mfma -optlc-fp-contract=fast+``` -#### 3D+> [!WARNING]+>+> 1. Results differ from a build without fma fusion by a few ULP.+> 2. Fusion decisions may vary across LLVM versions.+>    Skip this flag if you need bit-identical output across builds/toolchains.+> 3. You must use `-fllvm` to use this flag. It has no effect on the native+>    code generator. -| name        | values / second |-| ----------- | --------------- |-| value3      | 85_438_023      |-| perlin3     | 56_830_482      |-| valueCubic3 | 15_559_523      |+`-optlc-fp-contract=fast` lets LLVM fuse multiply-add chains into FMA+instructions, an optimization modern C++ compilers apply by default. This+gives a ~5-15% improvement on these kernels in testing. +### Parallel noise generation++This library integrates well with [massiv](https://hackage.haskell.org/package/massiv)+for parallel computation. Parallel evaluation reaches roughly 6-9x+single-threaded throughput on a 14-core machine in pinned-clock measurements.++> [!IMPORTANT]+>+> Massiv integration is the recommended approach for generating large noise+> textures or datasets.++### Benchmarks++#### Results++Measured by values / second generated by the noise functions, in the+`llvm-bench` configuration (LLVM backend + FP contraction), on an i7-1370P+**pinned at 1.9 GHz** for measurement stability —++Absolute figures scale with CPU clock. The FastNoiseLite ratios are intended+to be clock-invariant.++There's inevitably some noise in the measurements because the results are forced+into an unboxed vector.++> [!NOTE]+>+> These numbers are lower than the initial release because they were re-run on a+> slower processor. Order-of-magnitude/comparative difference remains reasonably+> stable. See the benchmark README for details.++##### 2D++| name          | Float (values/sec) | Double (values/sec) |+| ------------- | ------------------ | ------------------- |+| value2        | 64_407_126         | 68_260_653          |+| perlin2       | 61_301_663         | 65_143_707          |+| openSimplex2  | 25_982_291         | 27_045_472          |+| valueCubic2   | 22_743_642         | 23_403_842          |+| superSimplex2 | 17_167_069         | 17_762_669          |+| cellular2     | 16_025_950         | 16_007_044          |++##### 3D++| name          | Float (values/sec) | Double (values/sec) |+| ------------- | ------------------ | ------------------- |+| value3        | 34_673_623         | 35_929_146          |+| perlin3       | 29_325_590         | 30_432_482          |+| openSimplex3  | 10_975_857         | 10_922_644          |+| superSimplex3 | 9_232_128          | 9_166_843           |+| valueCubic3   | 7_453_365          | 7_278_612           |+| cellular3     | 5_238_497          | 5_061_911           |+ ## Examples -There's an interactive [demo app](demo/README.md) in the `demo` directory.+There's an interactive [demo app](https://github.com/jtnuttall/pure-noise/tree/main/demo) in the `demo` directory. -_OpenSimplex2_+### OpenSimplex2 -![OpenSimplex2](demo/images/opensimplex.png)-![OpenSimplex2 ridged](demo/images/opensimplex-ridged.png)+![OpenSimplex2](https://raw.githubusercontent.com/jtnuttall/pure-noise/main/demo/images/opensimplex.png)+![OpenSimplex2 ridged](https://raw.githubusercontent.com/jtnuttall/pure-noise/main/demo/images/opensimplex-ridged.png) -_Perlin_+### Perlin -![Perlin fBm](demo/images/perlin-fbm.png)+![Perlin fBm](https://raw.githubusercontent.com/jtnuttall/pure-noise/main/demo/images/perlin-fbm.png) -_Cellular_+### Cellular -![value](demo/images/cell-value.png)-![distance2add](demo/images/cell-d2.png)+![value](https://raw.githubusercontent.com/jtnuttall/pure-noise/main/demo/images/cell-value.png)+![distance2add](https://raw.githubusercontent.com/jtnuttall/pure-noise/main/demo/images/cell-d2.png)
bench/Bench.hs view
@@ -1,295 +1,457 @@ import BenchLib+import Data.Massiv.Array qualified as MA import Data.Typeable import Data.Vector.Unboxed qualified as U import Numeric.Noise-import Numeric.Noise.Internal (const2, const3)-import System.Random.MWC qualified as MWC+import System.Random.Stateful (StatefulGen, UniformRange, newAtomicGenM, newStdGen, uniformRM)  main :: IO () main = do   let sz = 1_000_000-      seed = 1337       octaves = 8+      massivW = 1_000+      massivH = 1_000   defaultMain     [ bgroup         "2D"-        ( baseline2 seed sz-            <> benchPerlin2 seed octaves sz-            <> benchOpenSimplex2 seed octaves sz-            <> benchOpenSimplexSmooth2 seed octaves sz-            <> benchValue2 seed octaves sz-            <> benchValueCubic2 seed octaves sz-            <> benchCombo2 seed octaves sz-            <> benchCellular2 seed octaves sz+        ( baseline2 sz+            <> benchPerlin2 octaves sz+            <> benchOpenSimplex2 octaves sz+            <> benchOpenSimplexSmooth2 octaves sz+            <> benchValue2 octaves sz+            <> benchValueCubic2 octaves sz+            <> benchCombo2 octaves sz+            <> benchCellular2 octaves sz         )     , bgroup         "3D"-        ( baseline3 seed sz-            <> benchPerlin3 seed octaves sz-            <> benchValue3 seed octaves sz-            <> benchValueCubic3 seed octaves sz+        ( baseline3 sz+            <> benchPerlin3 octaves sz+            <> benchOpenSimplex3 octaves sz+            <> benchSuperSimplex3 octaves sz+            <> benchValue3 octaves sz+            <> benchValueCubic3 octaves sz+            <> benchCellular3 sz         )+    , bgroup+        "2D massiv"+        ( benchMassivBase2 massivW massivH+            <> benchMassivFractal2 octaves massivW massivH+        )     ] -label :: (Typeable a) => String -> Int -> Seed -> Proxy a -> String-label lbl sz seed px =+label :: (Typeable a) => String -> Int -> Proxy a -> String+label lbl sz px =   let lbl' = case lbl of         "" -> ""         v -> v <> ": "-   in lbl' <> showsTypeRep (typeRep px) "" <> "[seed=" <> show seed <> "] x" <> show sz+   in lbl' <> showsTypeRep (typeRep px) "" <> " x" <> show sz -createEnv2 :: forall a. (U.Unbox a, MWC.UniformRange a, RealFrac a) => Int -> IO (U.Vector (a, a))+-- most of these functions zero at whole numbers and can short-circuit,+-- so a random offset should give a better signal of real world performance+generate2DCoords+  :: ( UniformRange a+     , RealFrac a+     , StatefulGen g IO+     )+  => g+  -> Int+  -> Int+  -> IO (a, a)+generate2DCoords g i j = do+  offsetX <- uniformRM (0.00001, 0.99999) g+  offsetY <- uniformRM (0.00001, 0.99999) g+  let r = fromIntegral i+      c = fromIntegral j++  pure (r + offsetX, c + offsetY)+{-# INLINE generate2DCoords #-}++createEnv2 :: forall a. (U.Unbox a, UniformRange a, RealFrac a) => Int -> IO (Seed, U.Vector (a, a)) createEnv2 sz = do-  g <- MWC.createSystemRandom-  U.generateM sz $ \i -> do-    -- most of these functions zero at whole numbers and can short-circuit,-    -- so a random offset should give a better signal of real world performance-    offset <- MWC.uniformRM (0.00001, 0.99999) g-    pure $-      let r = fromIntegral $ i `div` (sz `div` 2)-          c = fromIntegral $ i `mod` (sz `div` 2)-       in (r + offset, c + offset)+  g <- newAtomicGenM =<< newStdGen+  seed <- uniformRM (minBound, maxBound) g+  v <- U.generateM sz $ \i ->+    generate2DCoords+      g+      (i `div` (sz `div` 2))+      (i `mod` (sz `div` 2))+  pure (seed, v) {-# INLINE createEnv2 #-}  benchMany2   :: forall a-   . (Typeable a, MWC.UniformRange a, U.Unbox a, RealFrac a)+   . (Typeable a, UniformRange a, U.Unbox a, RealFrac a)   => String   -> Int-  -> Seed   -> Noise2 a   -> Benchmark-benchMany2 lbl sz seed f =-  env (createEnv2 sz) $ \ ~v ->-    bench (label lbl sz seed (Proxy @(U.Vector a))) $+benchMany2 lbl sz f =+  env (createEnv2 sz) $ \ ~(seed, v) ->+    bench (label lbl sz (Proxy @(U.Vector a))) $       nf (U.map (uncurry (noise2At f seed))) v {-# INLINE benchMany2 #-} -baseline2 :: Seed -> Int -> [Benchmark]-baseline2 seed sz =+baseline2 :: Int -> [Benchmark]+baseline2 sz =   [ bgroup       "baseline2"-      [ benchMany2 @Float "" sz seed (const2 1)-      , benchMany2 @Double "" sz seed (const2 2)+      [ benchMany2 @Float "" sz (const2 1)+      , benchMany2 @Double "" sz (const2 2)       ]   ]-{-# INLINE baseline2 #-} -benchPerlin2 :: Seed -> Int -> Int -> [Benchmark]-benchPerlin2 seed octaves sz =+benchPerlin2 :: Int -> Int -> [Benchmark]+benchPerlin2 octaves sz =   [ bgroup       "perlin2"-      [ benchMany2 @Float "" sz seed perlin2-      , benchMany2 @Double "" sz seed perlin2-      , benchMany2 @Float "fractal" sz seed (fractal2 defaultFractalConfig{octaves} perlin2)-      , benchMany2 @Double "fractal" sz seed (fractal2 defaultFractalConfig{octaves} perlin2)-      , benchMany2 @Float "ridged" sz seed (ridged2 defaultFractalConfig{octaves} perlin2)-      , benchMany2 @Double "ridged" sz seed (ridged2 defaultFractalConfig{octaves} perlin2)-      , benchMany2 @Float "billow" sz seed (billow2 defaultFractalConfig{octaves} perlin2)-      , benchMany2 @Double "billow" sz seed (billow2 defaultFractalConfig{octaves} perlin2)-      , benchMany2 @Float "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength perlin2)-      , benchMany2 @Double "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength perlin2)+      [ benchMany2 @Float "" sz perlin2+      , benchMany2 @Double "" sz perlin2+      , benchMany2 @Float "fractal" sz (fractal2 defaultFractalConfig{octaves} perlin2)+      , benchMany2 @Double "fractal" sz (fractal2 defaultFractalConfig{octaves} perlin2)+      , benchMany2 @Float "ridged" sz (ridged2 defaultFractalConfig{octaves} perlin2)+      , benchMany2 @Double "ridged" sz (ridged2 defaultFractalConfig{octaves} perlin2)+      , benchMany2 @Float "billow" sz (billow2 defaultFractalConfig{octaves} perlin2)+      , benchMany2 @Double "billow" sz (billow2 defaultFractalConfig{octaves} perlin2)+      , benchMany2 @Float "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength perlin2)+      , benchMany2 @Double "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength perlin2)       ]   ]-{-# INLINE benchPerlin2 #-} -benchOpenSimplex2 :: Seed -> Int -> Int -> [Benchmark]-benchOpenSimplex2 seed octaves sz =+benchOpenSimplex2 :: Int -> Int -> [Benchmark]+benchOpenSimplex2 octaves sz =   [ bgroup       "openSimplex2"-      [ benchMany2 @Float "" sz seed openSimplex2-      , benchMany2 @Double "" sz seed openSimplex2-      , benchMany2 @Float "fractal" sz seed (fractal2 defaultFractalConfig{octaves} openSimplex2)-      , benchMany2 @Double "fractal" sz seed (fractal2 defaultFractalConfig{octaves} openSimplex2)-      , benchMany2 @Float "ridged" sz seed (ridged2 defaultFractalConfig{octaves} openSimplex2)-      , benchMany2 @Double "ridged" sz seed (ridged2 defaultFractalConfig{octaves} openSimplex2)-      , benchMany2 @Float "billow" sz seed (billow2 defaultFractalConfig{octaves} openSimplex2)-      , benchMany2 @Double "billow" sz seed (billow2 defaultFractalConfig{octaves} openSimplex2)-      , benchMany2 @Float "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength openSimplex2)-      , benchMany2 @Double "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength openSimplex2)+      [ benchMany2 @Float "" sz openSimplex2+      , benchMany2 @Double "" sz openSimplex2+      , benchMany2 @Float "fractal" sz (fractal2 defaultFractalConfig{octaves} openSimplex2)+      , benchMany2 @Double "fractal" sz (fractal2 defaultFractalConfig{octaves} openSimplex2)+      , benchMany2 @Float "ridged" sz (ridged2 defaultFractalConfig{octaves} openSimplex2)+      , benchMany2 @Double "ridged" sz (ridged2 defaultFractalConfig{octaves} openSimplex2)+      , benchMany2 @Float "billow" sz (billow2 defaultFractalConfig{octaves} openSimplex2)+      , benchMany2 @Double "billow" sz (billow2 defaultFractalConfig{octaves} openSimplex2)+      , benchMany2 @Float "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength openSimplex2)+      , benchMany2 @Double "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength openSimplex2)       ]   ]-{-# INLINE benchOpenSimplex2 #-} -benchOpenSimplexSmooth2 :: Seed -> Int -> Int -> [Benchmark]-benchOpenSimplexSmooth2 seed octaves sz =+benchOpenSimplexSmooth2 :: Int -> Int -> [Benchmark]+benchOpenSimplexSmooth2 octaves sz =   [ bgroup       "superSimplex2"-      [ benchMany2 @Float "" sz seed superSimplex2-      , benchMany2 @Double "" sz seed superSimplex2-      , benchMany2 @Float "fractal" sz seed (fractal2 defaultFractalConfig{octaves} superSimplex2)-      , benchMany2 @Double "fractal" sz seed (fractal2 defaultFractalConfig{octaves} superSimplex2)-      , benchMany2 @Float "ridged" sz seed (ridged2 defaultFractalConfig{octaves} superSimplex2)-      , benchMany2 @Double "ridged" sz seed (ridged2 defaultFractalConfig{octaves} superSimplex2)-      , benchMany2 @Float "billow" sz seed (billow2 defaultFractalConfig{octaves} superSimplex2)-      , benchMany2 @Double "billow" sz seed (billow2 defaultFractalConfig{octaves} superSimplex2)-      , benchMany2 @Float "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength superSimplex2)-      , benchMany2 @Double "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength superSimplex2)+      [ benchMany2 @Float "" sz superSimplex2+      , benchMany2 @Double "" sz superSimplex2+      , benchMany2 @Float "fractal" sz (fractal2 defaultFractalConfig{octaves} superSimplex2)+      , benchMany2 @Double "fractal" sz (fractal2 defaultFractalConfig{octaves} superSimplex2)+      , benchMany2 @Float "ridged" sz (ridged2 defaultFractalConfig{octaves} superSimplex2)+      , benchMany2 @Double "ridged" sz (ridged2 defaultFractalConfig{octaves} superSimplex2)+      , benchMany2 @Float "billow" sz (billow2 defaultFractalConfig{octaves} superSimplex2)+      , benchMany2 @Double "billow" sz (billow2 defaultFractalConfig{octaves} superSimplex2)+      , benchMany2 @Float "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength superSimplex2)+      , benchMany2 @Double "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength superSimplex2)       ]   ]-{-# INLINE benchOpenSimplexSmooth2 #-} -benchValue2 :: Seed -> Int -> Int -> [Benchmark]-benchValue2 seed octaves sz =+benchValue2 :: Int -> Int -> [Benchmark]+benchValue2 octaves sz =   [ bgroup       "value2"-      [ benchMany2 @Float "" sz seed value2-      , benchMany2 @Double "" sz seed value2-      , benchMany2 @Float "fractal" sz seed (fractal2 defaultFractalConfig{octaves} value2)-      , benchMany2 @Double "fractal" sz seed (fractal2 defaultFractalConfig{octaves} value2)-      , benchMany2 @Float "ridged" sz seed (ridged2 defaultFractalConfig{octaves} value2)-      , benchMany2 @Double "ridged" sz seed (ridged2 defaultFractalConfig{octaves} value2)-      , benchMany2 @Float "billow" sz seed (billow2 defaultFractalConfig{octaves} value2)-      , benchMany2 @Double "billow" sz seed (billow2 defaultFractalConfig{octaves} value2)-      , benchMany2 @Float "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength value2)-      , benchMany2 @Double "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength value2)+      [ benchMany2 @Float "" sz value2+      , benchMany2 @Double "" sz value2+      , benchMany2 @Float "fractal" sz (fractal2 defaultFractalConfig{octaves} value2)+      , benchMany2 @Double "fractal" sz (fractal2 defaultFractalConfig{octaves} value2)+      , benchMany2 @Float "ridged" sz (ridged2 defaultFractalConfig{octaves} value2)+      , benchMany2 @Double "ridged" sz (ridged2 defaultFractalConfig{octaves} value2)+      , benchMany2 @Float "billow" sz (billow2 defaultFractalConfig{octaves} value2)+      , benchMany2 @Double "billow" sz (billow2 defaultFractalConfig{octaves} value2)+      , benchMany2 @Float "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength value2)+      , benchMany2 @Double "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength value2)       ]   ]-{-# INLINE benchValue2 #-} -benchValueCubic2 :: Seed -> Int -> Int -> [Benchmark]-benchValueCubic2 seed octaves sz =+benchValueCubic2 :: Int -> Int -> [Benchmark]+benchValueCubic2 octaves sz =   [ bgroup       "valueCubic2"-      [ benchMany2 @Float "" sz seed valueCubic2-      , benchMany2 @Double "" sz seed valueCubic2-      , benchMany2 @Float "fractal" sz seed (fractal2 defaultFractalConfig{octaves} valueCubic2)-      , benchMany2 @Double "fractal" sz seed (fractal2 defaultFractalConfig{octaves} valueCubic2)-      , benchMany2 @Float "ridged" sz seed (ridged2 defaultFractalConfig{octaves} valueCubic2)-      , benchMany2 @Double "ridged" sz seed (ridged2 defaultFractalConfig{octaves} valueCubic2)-      , benchMany2 @Float "billow" sz seed (billow2 defaultFractalConfig{octaves} valueCubic2)-      , benchMany2 @Double "billow" sz seed (billow2 defaultFractalConfig{octaves} valueCubic2)-      , benchMany2 @Float "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic2)-      , benchMany2 @Double "pingPong" sz seed (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic2)+      [ benchMany2 @Float "" sz valueCubic2+      , benchMany2 @Double "" sz valueCubic2+      , benchMany2 @Float "fractal" sz (fractal2 defaultFractalConfig{octaves} valueCubic2)+      , benchMany2 @Double "fractal" sz (fractal2 defaultFractalConfig{octaves} valueCubic2)+      , benchMany2 @Float "ridged" sz (ridged2 defaultFractalConfig{octaves} valueCubic2)+      , benchMany2 @Double "ridged" sz (ridged2 defaultFractalConfig{octaves} valueCubic2)+      , benchMany2 @Float "billow" sz (billow2 defaultFractalConfig{octaves} valueCubic2)+      , benchMany2 @Double "billow" sz (billow2 defaultFractalConfig{octaves} valueCubic2)+      , benchMany2 @Float "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic2)+      , benchMany2 @Double "pingPong" sz (pingPong2 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic2)       ]   ]-{-# INLINE benchValueCubic2 #-} -benchCombo2 :: Seed -> Int -> Int -> [Benchmark]-benchCombo2 seed octaves sz =+benchCombo2 :: Int -> Int -> [Benchmark]+benchCombo2 octaves sz =   [ bgroup       "numeric combination"-      [ benchMany2 @Float "perlin * opensimplex/2" sz seed $+      [ benchMany2 @Float "perlin * opensimplex/2" sz $           openSimplex2 / 2 * perlin2-      , benchMany2 @Float "(4 * perlin) / 4" sz seed $+      , benchMany2 @Float "(4 * perlin) / 4" sz $           4 * perlin2 / 4-      , benchMany2 @Float "(perlin + perlin + perlin + perlin) / 4" sz seed $+      , benchMany2 @Float "(perlin + perlin + perlin + perlin) / 4" sz $           (perlin2 + perlin2 + perlin2 + perlin2) / 4-      , benchMany2 @Float "fractal (perlin * opensimplex/2)" sz seed $+      , benchMany2 @Float "fractal (perlin * opensimplex/2)" sz $           fractal2 defaultFractalConfig{octaves} (openSimplex2 / 2 * perlin2)-      , benchMany2 @Float "fractal perlin * fractal opensimplex" sz seed $+      , benchMany2 @Float "fractal perlin * fractal opensimplex" sz $           fractal2 defaultFractalConfig{octaves} perlin2             * fractal2 defaultFractalConfig{octaves} openSimplex2       ]   ]-{-# INLINE benchCombo2 #-} -benchCellular2 :: Seed -> Int -> Int -> [Benchmark]-benchCellular2 seed _ sz =+benchCellular2 :: Int -> Int -> [Benchmark]+benchCellular2 _ sz =   [ bgroup       "cellular2"-      ( benches @Float Proxy-          <> benches @Double Proxy-      )+      [ benchMany2 @Float+          "DistEuclidean CellValue"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = CellValue})+      , benchMany2 @Float+          "DistEuclidean Distance2Add"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = Distance2Add})+      , benchMany2 @Float+          "DistManhattan CellValue"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistManhattan, cellularResult = CellValue})+      , benchMany2 @Float+          "DistManhattan Distance2Add"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistManhattan, cellularResult = Distance2Add})+      , benchMany2 @Double+          "DistEuclidean CellValue"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = CellValue})+      , benchMany2 @Double+          "DistEuclidean Distance2Add"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = Distance2Add})+      , benchMany2 @Double+          "DistManhattan CellValue"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistManhattan, cellularResult = CellValue})+      , benchMany2 @Double+          "DistManhattan Distance2Add"+          sz+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistManhattan, cellularResult = Distance2Add})+      ]   ]- where-  benches-    :: forall a. (Typeable a, MWC.UniformRange a, U.Unbox a, RealFrac a, Floating a) => Proxy a -> [Benchmark]-  benches _ =-    [ benchMany2 @a (show d <> " " <> show r) sz seed (cellular2 config)-    | d <- [DistEuclidean]-    , r <- [CellValue, Distance2Add]-    , let config = defaultCellularConfig{cellularDistanceFn = d, cellularResult = r}-    ]-  {-# INLINE benches #-}-{-# INLINE benchCellular2 #-} -createEnv3 :: forall a m. (Monad m, U.Unbox a, Num a) => Int -> m (U.Vector (a, a, a))+-- offsets are drawn per element (like createEnv2) and the strides are+-- independent per axis; the previous version drew one offset triple and+-- collapsed the index math to ~4 distinct points+createEnv3 :: (U.Unbox a, UniformRange a, RealFrac a) => Int -> IO (Seed, U.Vector (a, a, a)) createEnv3 sz = do-  !ixs <- U.generateM sz $ \i ->-    pure $-      let d = sz `div` 3-          !x = fromIntegral $ i `div` d `mod` d-          !y = fromIntegral $ i `div` (d * d)-          !z = fromIntegral $ i `div` d-       in (x, y, z)-  pure ixs+  g <- newAtomicGenM =<< newStdGen+  seed <- uniformRM (minBound, maxBound) g+  let d = ceiling (fromIntegral sz ** (1 / 3) :: Double)+  !ixs <- U.generateM sz $ \i -> do+    offsetX <- uniformRM (0.00001, 0.99999) g+    offsetY <- uniformRM (0.00001, 0.99999) g+    offsetZ <- uniformRM (0.00001, 0.99999) g+    let !x = fromIntegral (i `mod` d)+        !y = fromIntegral ((i `div` d) `mod` d)+        !z = fromIntegral (i `div` (d * d))+    pure (x + offsetX, y + offsetY, z + offsetZ)+  pure (seed, ixs) {-# INLINE createEnv3 #-}  benchMany3   :: forall a-   . (Typeable a, RealFrac a, U.Unbox a)+   . (Typeable a, UniformRange a, RealFrac a, U.Unbox a)   => String   -> Int-  -> Seed   -> Noise3 a   -> Benchmark-benchMany3 lbl sz seed f =-  env (createEnv3 sz) $ \ ~v ->-    bench (label lbl sz seed (Proxy @(U.Vector a))) $+benchMany3 lbl sz f =+  env (createEnv3 sz) $ \ ~(seed, v) ->+    bench (label lbl sz (Proxy @(U.Vector a))) $       nf (U.map (\(x, y, z) -> noise3At f seed x y z)) v {-# INLINE benchMany3 #-} -baseline3 :: Seed -> Int -> [Benchmark]-baseline3 seed sz =+baseline3 :: Int -> [Benchmark]+baseline3 sz =   [ bgroup       "baseline3"-      [ benchMany3 @Float "" sz seed (const3 1)-      , benchMany3 @Double "" sz seed (const3 2)+      [ benchMany3 @Float "" sz (const3 1)+      , benchMany3 @Double "" sz (const3 2)       ]   ]-{-# INLINE baseline3 #-} -benchPerlin3 :: Seed -> Int -> Int -> [Benchmark]-benchPerlin3 seed octaves sz =+benchPerlin3 :: Int -> Int -> [Benchmark]+benchPerlin3 octaves sz =   [ bgroup       "perlin3"-      [ benchMany3 @Float "" sz seed perlin3-      , benchMany3 @Double "" sz seed perlin3-      , benchMany3 @Float "fractal" sz seed (fractal3 defaultFractalConfig{octaves} perlin3)-      , benchMany3 @Double "fractal" sz seed (fractal3 defaultFractalConfig{octaves} perlin3)-      , benchMany3 @Float "ridged" sz seed (ridged3 defaultFractalConfig{octaves} perlin3)-      , benchMany3 @Double "ridged" sz seed (ridged3 defaultFractalConfig{octaves} perlin3)-      , benchMany3 @Float "billow" sz seed (billow3 defaultFractalConfig{octaves} perlin3)-      , benchMany3 @Double "billow" sz seed (billow3 defaultFractalConfig{octaves} perlin3)-      , benchMany3 @Float "pingPong" sz seed (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength perlin3)-      , benchMany3 @Double "pingPong" sz seed (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength perlin3)+      [ benchMany3 @Float "" sz perlin3+      , benchMany3 @Double "" sz perlin3+      , benchMany3 @Float "fractal" sz (fractal3 defaultFractalConfig{octaves} perlin3)+      , benchMany3 @Double "fractal" sz (fractal3 defaultFractalConfig{octaves} perlin3)+      , benchMany3 @Float "ridged" sz (ridged3 defaultFractalConfig{octaves} perlin3)+      , benchMany3 @Double "ridged" sz (ridged3 defaultFractalConfig{octaves} perlin3)+      , benchMany3 @Float "billow" sz (billow3 defaultFractalConfig{octaves} perlin3)+      , benchMany3 @Double "billow" sz (billow3 defaultFractalConfig{octaves} perlin3)+      , benchMany3 @Float "pingPong" sz (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength perlin3)+      , benchMany3 @Double "pingPong" sz (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength perlin3)       ]   ]-{-# INLINE benchPerlin3 #-} -benchValue3 :: Seed -> Int -> Int -> [Benchmark]-benchValue3 seed octaves sz =+benchOpenSimplex3 :: Int -> Int -> [Benchmark]+benchOpenSimplex3 octaves sz =   [ bgroup+      "openSimplex3"+      [ benchMany3 @Float "" sz openSimplex3+      , benchMany3 @Double "" sz openSimplex3+      , benchMany3 @Float "fractal" sz (fractal3 defaultFractalConfig{octaves} openSimplex3)+      , benchMany3 @Double "fractal" sz (fractal3 defaultFractalConfig{octaves} openSimplex3)+      ]+  ]++benchSuperSimplex3 :: Int -> Int -> [Benchmark]+benchSuperSimplex3 octaves sz =+  [ bgroup+      "superSimplex3"+      [ benchMany3 @Float "" sz superSimplex3+      , benchMany3 @Double "" sz superSimplex3+      , benchMany3 @Float "fractal" sz (fractal3 defaultFractalConfig{octaves} superSimplex3)+      , benchMany3 @Double "fractal" sz (fractal3 defaultFractalConfig{octaves} superSimplex3)+      ]+  ]++benchCellular3 :: Int -> [Benchmark]+benchCellular3 sz =+  [ bgroup+      "cellular3"+      [ benchMany3 @Float+          "DistEuclidean CellValue"+          sz+          (cellular3 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = CellValue})+      , benchMany3 @Float+          "DistEuclidean Distance2Add"+          sz+          (cellular3 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = Distance2Add})+      , benchMany3 @Double+          "DistEuclidean CellValue"+          sz+          (cellular3 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = CellValue})+      , benchMany3 @Double+          "DistEuclidean Distance2Add"+          sz+          (cellular3 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = Distance2Add})+      ]+  ]++benchValue3 :: Int -> Int -> [Benchmark]+benchValue3 octaves sz =+  [ bgroup       "value3"-      [ benchMany3 @Float "" sz seed value3-      , benchMany3 @Double "" sz seed value3-      , benchMany3 @Float "fractal" sz seed (fractal3 defaultFractalConfig{octaves} value3)-      , benchMany3 @Double "fractal" sz seed (fractal3 defaultFractalConfig{octaves} value3)-      , benchMany3 @Float "ridged" sz seed (ridged3 defaultFractalConfig{octaves} value3)-      , benchMany3 @Double "ridged" sz seed (ridged3 defaultFractalConfig{octaves} value3)-      , benchMany3 @Float "billow" sz seed (billow3 defaultFractalConfig{octaves} value3)-      , benchMany3 @Double "billow" sz seed (billow3 defaultFractalConfig{octaves} value3)-      , benchMany3 @Float "pingPong" sz seed (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength value3)-      , benchMany3 @Double "pingPong" sz seed (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength value3)+      [ benchMany3 @Float "" sz value3+      , benchMany3 @Double "" sz value3+      , benchMany3 @Float "fractal" sz (fractal3 defaultFractalConfig{octaves} value3)+      , benchMany3 @Double "fractal" sz (fractal3 defaultFractalConfig{octaves} value3)+      , benchMany3 @Float "ridged" sz (ridged3 defaultFractalConfig{octaves} value3)+      , benchMany3 @Double "ridged" sz (ridged3 defaultFractalConfig{octaves} value3)+      , benchMany3 @Float "billow" sz (billow3 defaultFractalConfig{octaves} value3)+      , benchMany3 @Double "billow" sz (billow3 defaultFractalConfig{octaves} value3)+      , benchMany3 @Float "pingPong" sz (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength value3)+      , benchMany3 @Double "pingPong" sz (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength value3)       ]   ]-{-# INLINE benchValue3 #-} -benchValueCubic3 :: Seed -> Int -> Int -> [Benchmark]-benchValueCubic3 seed octaves sz =+benchValueCubic3 :: Int -> Int -> [Benchmark]+benchValueCubic3 octaves sz =   [ bgroup       "valueCubic3"-      [ benchMany3 @Float "" sz seed valueCubic3-      , benchMany3 @Double "" sz seed valueCubic3-      , benchMany3 @Float "fractal" sz seed (fractal3 defaultFractalConfig{octaves} valueCubic3)-      , benchMany3 @Double "fractal" sz seed (fractal3 defaultFractalConfig{octaves} valueCubic3)-      , benchMany3 @Float "ridged" sz seed (ridged3 defaultFractalConfig{octaves} valueCubic3)-      , benchMany3 @Double "ridged" sz seed (ridged3 defaultFractalConfig{octaves} valueCubic3)-      , benchMany3 @Float "billow" sz seed (billow3 defaultFractalConfig{octaves} valueCubic3)-      , benchMany3 @Double "billow" sz seed (billow3 defaultFractalConfig{octaves} valueCubic3)-      , benchMany3 @Float "pingPong" sz seed (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic3)-      , benchMany3 @Double "pingPong" sz seed (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic3)+      [ benchMany3 @Float "" sz valueCubic3+      , benchMany3 @Double "" sz valueCubic3+      , benchMany3 @Float "fractal" sz (fractal3 defaultFractalConfig{octaves} valueCubic3)+      , benchMany3 @Double "fractal" sz (fractal3 defaultFractalConfig{octaves} valueCubic3)+      , benchMany3 @Float "ridged" sz (ridged3 defaultFractalConfig{octaves} valueCubic3)+      , benchMany3 @Double "ridged" sz (ridged3 defaultFractalConfig{octaves} valueCubic3)+      , benchMany3 @Float "billow" sz (billow3 defaultFractalConfig{octaves} valueCubic3)+      , benchMany3 @Double "billow" sz (billow3 defaultFractalConfig{octaves} valueCubic3)+      , benchMany3 @Float "pingPong" sz (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic3)+      , benchMany3 @Double "pingPong" sz (pingPong3 defaultFractalConfig{octaves} defaultPingPongStrength valueCubic3)       ]   ]-{-# INLINE benchValueCubic3 #-}++benchMassiv2+  :: forall a+   . (Typeable a, U.Unbox a, RealFrac a, UniformRange a)+  => String+  -> Int+  -> Int+  -> Noise2 a+  -> Benchmark+benchMassiv2 lbl !w !h noiseF =+  env+    ( do+        g <- newAtomicGenM =<< newStdGen+        seed <- uniformRM (minBound, maxBound) g+        -- This intentionally breaks the optimizer's ability to DCE. If we try to calculate+        -- inline it seems that GHC is smart enough to figure out that the whole-number+        -- integral points involve relatively simple code paths.+        (arr :: MA.Array MA.U MA.Ix2 (a, a)) <-+          MA.generateArray @MA.U MA.Par (MA.Sz2 h w) $ \(i MA.:. j) ->+            generate2DCoords g i j++        pure (seed, arr)+    )+    $ \ ~(seed, arr) ->+      bench (label lbl (w * h) (Proxy @a)) $+        nf+          ( MA.computeP @MA.U+              . MA.map+                ( \(!x, !y) ->+                    noise2At noiseF seed x y+                )+          )+          arr+{-# INLINE benchMassiv2 #-}++benchMassivBase2 :: Int -> Int -> [Benchmark]+benchMassivBase2 !w !h =+  [ bgroup+      "massiv base2"+      [ benchMassiv2 @Float "perlin2" w h perlin2+      , benchMassiv2 @Double "perlin2" w h perlin2+      , benchMassiv2 @Float "openSimplex2" w h openSimplex2+      , benchMassiv2 @Double "openSimplex2" w h openSimplex2+      , benchMassiv2 @Float "superSimplex2" w h superSimplex2+      , benchMassiv2 @Double "superSimplex2" w h superSimplex2+      , benchMassiv2 @Float "value2" w h value2+      , benchMassiv2 @Double "value2" w h value2+      , benchMassiv2 @Float "valueCubic2" w h valueCubic2+      , benchMassiv2 @Double "valueCubic2" w h valueCubic2+      , benchMassiv2 @Float+          "cellular2"+          w+          h+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = CellValue})+      , benchMassiv2 @Double+          "cellular2"+          w+          h+          (cellular2 defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = CellValue})+      ]+  ]++benchMassivFractal2 :: Int -> Int -> Int -> [Benchmark]+benchMassivFractal2 octaves w h =+  [ bgroup+      "massiv fractal2"+      [ benchMassiv2 @Float "perlin2 fractal" w h (fractal2 defaultFractalConfig{octaves} perlin2)+      , benchMassiv2 @Double "perlin2 fractal" w h (fractal2 defaultFractalConfig{octaves} perlin2)+      , benchMassiv2 @Float "value2 fractal" w h (fractal2 defaultFractalConfig{octaves} value2)+      , benchMassiv2 @Double "value2 fractal" w h (fractal2 defaultFractalConfig{octaves} value2)+      , benchMassiv2 @Float "openSimplex2 fractal" w h (fractal2 defaultFractalConfig{octaves} openSimplex2)+      , benchMassiv2 @Double "openSimplex2 fractal" w h (fractal2 defaultFractalConfig{octaves} openSimplex2)+      , benchMassiv2 @Float "superSimplex2 fractal" w h (fractal2 defaultFractalConfig{octaves} superSimplex2)+      , benchMassiv2 @Double "superSimplex2 fractal" w h (fractal2 defaultFractalConfig{octaves} superSimplex2)+      ]+  ]
bench/BenchLib.hs view
+ bench/fnl-compare/FnlBench.hs view
@@ -0,0 +1,234 @@+-- | Performance comparison against the vendored FastNoiseLite+--+-- Ratios are printed by tasty-bench's 'bcompare': each @pure-noise@ line ends+-- with e.g. @1.05x@ = its mean time relative to the matching @fnl@ line+-- (lower is better; 1.05x means pure-noise is 5% slower).+--+-- Ratios only print when the matching fnl benchmark runs in the same invocation,+-- so filter by group (e.g. @-p \/perlin\/@), not by side.+module Main (main) where++import Control.Monad.State.Strict (evalState, state)+import Data.Vector.Storable qualified as S+import Foreign.C.Types (CFloat (..), CInt (..))+import Foreign.Ptr (Ptr)+import Numeric.Noise+import System.Random.SplitMix (SMGen, mkSMGen, nextFloat)+import Test.Tasty.Bench+import Test.Tasty.Patterns.Printer (printAwkExpr)++main :: IO ()+main =+  defaultMain (map (mapLeafBenchmarks addCompare) benchmarks)++-- | Attach a bcompare ratio to every pure-noise leaf, targeting the fnl leaf+-- in the same group (the pattern matches exactly one benchmark).+addCompare :: [String] -> Benchmark -> Benchmark+addCompare (leaf : path) b+  | leaf == pnLeaf = bcompare (printAwkExpr (locateBenchmark (fnlLeaf : path))) b+addCompare _ b = b++fnlLeaf, pnLeaf :: String+fnlLeaf = "fnl x" <> show samples+pnLeaf = "pure-noise x" <> show samples++benchmarks :: [Benchmark]+benchmarks =+  [ env mkEnv2 $ \ ~(grid, rand, kOne, kSmall) ->+      bgroup+        "2D"+        [ algo2 grid rand kOne kSmall "value" fnlValue value2+        , algo2 grid rand kOne kSmall "valueCubic" fnlValueCubic valueCubic2+        , algo2 grid rand kOne kSmall "perlin" fnlPerlin perlin2+        , algo2 grid rand kOne kSmall "openSimplex2" fnlOpenSimplex2 openSimplex2+        , algo2 grid rand kOne kSmall "superSimplex2" fnlOpenSimplex2S superSimplex2+        , algo2 grid rand kOne kSmall "cellular" fnlCellular (cellular2 benchCellularConfig)+        ]+  , env mkEnv3 $ \ ~(grid, rand, kOne, kSmall) ->+      bgroup+        "3D"+        [ algo3 grid rand kOne kSmall "value" fnlValue value3+        , algo3 grid rand kOne kSmall "valueCubic" fnlValueCubic valueCubic3+        , algo3 grid rand kOne kSmall "perlin" fnlPerlin perlin3+        , algo3 grid rand kOne kSmall "openSimplex2" fnlOpenSimplex2 openSimplex3+        , algo3 grid rand kOne kSmall "superSimplex2" fnlOpenSimplex2S superSimplex3+        , algo3 grid rand kOne kSmall "cellular" fnlCellular (cellular3 benchCellularConfig)+        ]+  ]++algo2+  :: (S.Vector Float, S.Vector Float)+  -> (S.Vector Float, S.Vector Float)+  -> Float+  -> Float+  -> String+  -> CInt+  -> Noise2 Float+  -> Benchmark+algo2 grid rand kOne kSmall name ty nz =+  bgroup+    name+    [ bgroup "grid" (pair grid kOne)+    , bgroup "freq001" (pair grid kSmall)+    , bgroup "random" (pair rand kOne)+    ]+ where+  pair ~(xs, ys) k =+    [ bench fnlLeaf $ whnfIO (fnlSum2 ty k xs ys)+    , bench pnLeaf $ whnf (\kk -> sumNoise2 nz kk xs ys) k+    ]+{-# INLINE algo2 #-}++algo3+  :: (S.Vector Float, S.Vector Float, S.Vector Float)+  -> (S.Vector Float, S.Vector Float, S.Vector Float)+  -> Float+  -> Float+  -> String+  -> CInt+  -> Noise3 Float+  -> Benchmark+algo3 grid rand kOne kSmall name ty nz =+  bgroup+    name+    [ bgroup "grid" (pair grid kOne)+    , bgroup "freq001" (pair grid kSmall)+    , bgroup "random" (pair rand kOne)+    ]+ where+  -- lazy pattern: see algo2+  pair ~(xs, ys, zs) k =+    [ bench fnlLeaf $ whnfIO (fnlSum3 ty k xs ys zs)+    , bench pnLeaf $ whnf (\kk -> sumNoise3 nz kk xs ys zs) k+    ]+{-# INLINE algo3 #-}++----------------------------------------------------------------------------------------------------+-- Matched sweeps+----------------------------------------------------------------------------------------------------++sumNoise2 :: Noise2 Float -> Float -> S.Vector Float -> S.Vector Float -> Float+sumNoise2 nz k xs ys = go 0 0+ where+  !n = S.length xs+  go !i !acc+    | i >= n = acc+    | otherwise =+        go (i + 1) (acc + noise2At nz benchSeed (k * S.unsafeIndex xs i) (k * S.unsafeIndex ys i))+{-# INLINE sumNoise2 #-}++sumNoise3 :: Noise3 Float -> Float -> S.Vector Float -> S.Vector Float -> S.Vector Float -> Float+sumNoise3 nz k xs ys zs = go 0 0+ where+  !n = S.length xs+  go !i !acc+    | i >= n = acc+    | otherwise =+        go+          (i + 1)+          (acc + noise3At nz benchSeed (k * S.unsafeIndex xs i) (k * S.unsafeIndex ys i) (k * S.unsafeIndex zs i))+{-# INLINE sumNoise3 #-}++----------------------------------------------------------------------------------------------------+-- FFI (fnl_bench_shim.cpp)+----------------------------------------------------------------------------------------------------++foreign import ccall unsafe "fnl_bench_sum2"+  c_fnlSum2 :: CInt -> CInt -> CFloat -> CInt -> Ptr Float -> Ptr Float -> IO CFloat++foreign import ccall unsafe "fnl_bench_sum3"+  c_fnlSum3 :: CInt -> CInt -> CFloat -> CInt -> Ptr Float -> Ptr Float -> Ptr Float -> IO CFloat++fnlSum2 :: CInt -> Float -> S.Vector Float -> S.Vector Float -> IO Float+fnlSum2 ty k xs ys =+  S.unsafeWith xs $ \px ->+    S.unsafeWith ys $ \py -> do+      CFloat r <- c_fnlSum2 ty fnlBenchSeed (CFloat k) (fromIntegral (S.length xs)) px py+      pure r++fnlSum3 :: CInt -> Float -> S.Vector Float -> S.Vector Float -> S.Vector Float -> IO Float+fnlSum3 ty k xs ys zs =+  S.unsafeWith xs $ \px ->+    S.unsafeWith ys $ \py ->+      S.unsafeWith zs $ \pz -> do+        CFloat r <- c_fnlSum3 ty fnlBenchSeed (CFloat k) (fromIntegral (S.length xs)) px py pz+        pure r++fnlOpenSimplex2, fnlOpenSimplex2S, fnlCellular, fnlPerlin, fnlValueCubic, fnlValue :: CInt+fnlOpenSimplex2 = 0+fnlOpenSimplex2S = 1+fnlCellular = 2+fnlPerlin = 3+fnlValueCubic = 4+fnlValue = 5++-- 1337 is the FNL bench convention.+benchSeed :: Seed+benchSeed = 1337++fnlBenchSeed :: CInt+fnlBenchSeed = 1337++benchCellularConfig :: CellularConfig Float+benchCellularConfig = defaultCellularConfig{cellularDistanceFn = DistEuclidean, cellularResult = Distance}++-- ---------------------------------------------------------------------------+-- Coordinate environments (built once per dimension)+-- ---------------------------------------------------------------------------++-- n = 262144 everywhere: 512*512 (2D grid), 64^3 (3D grid), and the random+-- streams, so every leaf carries the same "xN" count for vps.py.+gridSize2, gridSize3, samples :: Int+gridSize2 = 512+gridSize3 = 64+samples = gridSize2 * gridSize2++-- (grid xs/ys, random xs/ys, kOne = 1.0, kSmall = 0.01). The ks come out of+-- the IO action so the simplifier cannot constant-fold the per-point multiply+-- on the Haskell side only.+mkEnv2 :: IO ((S.Vector Float, S.Vector Float), (S.Vector Float, S.Vector Float), Float, Float)+mkEnv2 = pure (mkGrid2, mkRand2 samples, 1.0, 0.01)++mkEnv3+  :: IO+       ( (S.Vector Float, S.Vector Float, S.Vector Float)+       , (S.Vector Float, S.Vector Float, S.Vector Float)+       , Float+       , Float+       )+mkEnv3 = pure (mkGrid3, mkRand3 samples, 1.0, 0.01)++-- Integer lattice in FNL benchmark loop order (x fastest, then y, then z).+mkGrid2 :: (S.Vector Float, S.Vector Float)+mkGrid2 =+  ( S.generate samples (\i -> fromIntegral (i `mod` gridSize2))+  , S.generate samples (\i -> fromIntegral (i `div` gridSize2))+  )++mkGrid3 :: (S.Vector Float, S.Vector Float, S.Vector Float)+mkGrid3 =+  ( S.generate samples (\i -> fromIntegral (i `mod` gridSize3))+  , S.generate samples (\i -> fromIntegral ((i `div` gridSize3) `mod` gridSize3))+  , S.generate samples (\i -> fromIntegral (i `div` (gridSize3 * gridSize3)))+  )++smgen :: SMGen+smgen = mkSMGen 0x9E3779B97F4A7C15++draws :: Int -> S.Vector Float+draws n = S.map (* 512) . evalState (S.generateM n . const . state $ nextFloat) $ smgen++mkRand2 :: Int -> (S.Vector Float, S.Vector Float)+mkRand2 n =+  let v = draws (2 * n)+   in ( S.generate n (\i -> v S.! (2 * i))+      , S.generate n (\i -> v S.! (2 * i + 1))+      )++mkRand3 :: Int -> (S.Vector Float, S.Vector Float, S.Vector Float)+mkRand3 n =+  let v = draws (3 * n)+   in ( S.generate n (\i -> v S.! (3 * i))+      , S.generate n (\i -> v S.! (3 * i + 1))+      , S.generate n (\i -> v S.! (3 * i + 2))+      )
+ bench/fnl-compare/cbits/FastNoiseLite.h view
@@ -0,0 +1,2586 @@+// MIT License+//+// Copyright(c) 2023 Jordan Peck (jordan.me2@gmail.com)+// Copyright(c) 2023 Contributors+//+// Permission is hereby granted, free of charge, to any person obtaining a copy+// of this software and associated documentation files(the "Software"), to deal+// in the Software without restriction, including without limitation the rights+// to use, copy, modify, merge, publish, distribute, sublicense, and / or sell+// copies of the Software, and to permit persons to whom the Software is+// furnished to do so, subject to the following conditions :+//+// The above copyright notice and this permission notice shall be included in all+// copies or substantial portions of the Software.+//+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE+// SOFTWARE.+//+// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'...        ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll+// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'....       ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo+// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd+// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx+// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'...      ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx+// . ....';:cloddddo___________,,,,;;:clooddddoolc:,...      ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd+// .......',;:cccc:|           |,,,;;:cclooddddoll:;'..     ..';cox|  \KKK000|   |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo+// .......'',,,,,''|   ________|',,;;::cclloooooolc:;'......___:ldk|   \KK000|   |XKKK0Okxolc|   |;;::cclodxxkkkkxxdoolllcclllooodddooooo+// ''......''''....|   |  ....'',,,,;;;::cclloooollc:;,''.'|   |oxk|    \OOO0|   |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo+// ;;,''.......... |   |_____',,;;;____:___cllo________.___|   |___|     \xkk|   |KK_______ool___:::;________;;;_______...'',;;:ccclllloo+// c:;,''......... |         |:::/     '   |lo/        |           |      \dx|   |0/       \d|   |cc/        |'/       \......',,;;:ccllo+// ol:;,'..........|    _____|ll/    __    |o/   ______|____    ___|   |   \o|   |/   ___   \|   |o/   ______|/   ___   \ .......'',;:clo+// dlc;,...........|   |::clooo|    /  |   |x\___   \KXKKK0|   |dol|   |\   \|   |   |   |   |   |d\___   \..|   |  /   /       ....',:cl+// xoc;'...  .....'|   |llodddd|    \__|   |_____\   \KKK0O|   |lc:|   |'\       |   |___|   |   |_____\   \.|   |_/___/...      ...',;:c+// dlc;'... ....',;|   |oddddddo\          |          |Okkx|   |::;|   |..\      |\         /|   |          | \         |...    ....',;:c+// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc+// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll+// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo+// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd+// .    .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk+//       ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000+//       ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX+//+// VERSION: 1.1.1+// https://github.com/Auburn/FastNoiseLite++#ifndef FASTNOISELITE_H+#define FASTNOISELITE_H++#include <cmath>++class FastNoiseLite+{+public:+    enum NoiseType+    {+        NoiseType_OpenSimplex2,+        NoiseType_OpenSimplex2S,+        NoiseType_Cellular,+        NoiseType_Perlin,+        NoiseType_ValueCubic,+        NoiseType_Value+    };++    enum RotationType3D+    {+        RotationType3D_None,+        RotationType3D_ImproveXYPlanes,+        RotationType3D_ImproveXZPlanes+    };++    enum FractalType+    {+        FractalType_None,+        FractalType_FBm,+        FractalType_Ridged,+        FractalType_PingPong,+        FractalType_DomainWarpProgressive,+        FractalType_DomainWarpIndependent+    };++    enum CellularDistanceFunction+    {+        CellularDistanceFunction_Euclidean,+        CellularDistanceFunction_EuclideanSq,+        CellularDistanceFunction_Manhattan,+        CellularDistanceFunction_Hybrid+    };++    enum CellularReturnType+    {+        CellularReturnType_CellValue,+        CellularReturnType_Distance,+        CellularReturnType_Distance2,+        CellularReturnType_Distance2Add,+        CellularReturnType_Distance2Sub,+        CellularReturnType_Distance2Mul,+        CellularReturnType_Distance2Div+    };++    enum DomainWarpType+    {+        DomainWarpType_OpenSimplex2,+        DomainWarpType_OpenSimplex2Reduced,+        DomainWarpType_BasicGrid+    };++    /// <summary>+    /// Create new FastNoise object with optional seed+    /// </summary>+    FastNoiseLite(int seed = 1337)+    {+        mSeed = seed;+        mFrequency = 0.01f;+        mNoiseType = NoiseType_OpenSimplex2;+        mRotationType3D = RotationType3D_None;+        mTransformType3D = TransformType3D_DefaultOpenSimplex2;++        mFractalType = FractalType_None;+        mOctaves = 3;+        mLacunarity = 2.0f;+        mGain = 0.5f;+        mWeightedStrength = 0.0f;+        mPingPongStrength = 2.0f;++        mFractalBounding = 1 / 1.75f;++        mCellularDistanceFunction = CellularDistanceFunction_EuclideanSq;+        mCellularReturnType = CellularReturnType_Distance;+        mCellularJitterModifier = 1.0f;++        mDomainWarpType = DomainWarpType_OpenSimplex2;+        mWarpTransformType3D = TransformType3D_DefaultOpenSimplex2;+        mDomainWarpAmp = 1.0f;+    }++    /// <summary>+    /// Sets seed used for all noise types+    /// </summary>+    /// <remarks>+    /// Default: 1337+    /// </remarks>+    void SetSeed(int seed) { mSeed = seed; }++    /// <summary>+    /// Sets frequency for all noise types+    /// </summary>+    /// <remarks>+    /// Default: 0.01+    /// </remarks>+    void SetFrequency(float frequency) { mFrequency = frequency; }++    /// <summary>+    /// Sets noise algorithm used for GetNoise(...)+    /// </summary>+    /// <remarks>+    /// Default: OpenSimplex2+    /// </remarks>+    void SetNoiseType(NoiseType noiseType)+    {+        mNoiseType = noiseType;+        UpdateTransformType3D();+    }++    /// <summary>+    /// Sets domain rotation type for 3D Noise and 3D DomainWarp.+    /// Can aid in reducing directional artifacts when sampling a 2D plane in 3D+    /// </summary>+    /// <remarks>+    /// Default: None+    /// </remarks>+    void SetRotationType3D(RotationType3D rotationType3D)+    {+        mRotationType3D = rotationType3D;+        UpdateTransformType3D();+        UpdateWarpTransformType3D();+    }++    /// <summary>+    /// Sets method for combining octaves in all fractal noise types+    /// </summary>+    /// <remarks>+    /// Default: None+    /// Note: FractalType_DomainWarp... only affects DomainWarp(...)+    /// </remarks>+    void SetFractalType(FractalType fractalType) { mFractalType = fractalType; }++    /// <summary>+    /// Sets octave count for all fractal noise types +    /// </summary>+    /// <remarks>+    /// Default: 3+    /// </remarks>+    void SetFractalOctaves(int octaves)+    {+        mOctaves = octaves;+        CalculateFractalBounding();+    }++    /// <summary>+    /// Sets octave lacunarity for all fractal noise types+    /// </summary>+    /// <remarks>+    /// Default: 2.0+    /// </remarks>+    void SetFractalLacunarity(float lacunarity) { mLacunarity = lacunarity; }++    /// <summary>+    /// Sets octave gain for all fractal noise types+    /// </summary>+    /// <remarks>+    /// Default: 0.5+    /// </remarks>+    void SetFractalGain(float gain)+    {+        mGain = gain;+        CalculateFractalBounding();+    }++    /// <summary>+    /// Sets octave weighting for all none DomainWarp fratal types+    /// </summary>+    /// <remarks>+    /// Default: 0.0+    /// Note: Keep between 0...1 to maintain -1...1 output bounding+    /// </remarks>+    void SetFractalWeightedStrength(float weightedStrength) { mWeightedStrength = weightedStrength; }++    /// <summary>+    /// Sets strength of the fractal ping pong effect+    /// </summary>+    /// <remarks>+    /// Default: 2.0+    /// </remarks>+    void SetFractalPingPongStrength(float pingPongStrength) { mPingPongStrength = pingPongStrength; }+++    /// <summary>+    /// Sets distance function used in cellular noise calculations+    /// </summary>+    /// <remarks>+    /// Default: Distance+    /// </remarks>+    void SetCellularDistanceFunction(CellularDistanceFunction cellularDistanceFunction) { mCellularDistanceFunction = cellularDistanceFunction; }++    /// <summary>+    /// Sets return type from cellular noise calculations+    /// </summary>+    /// <remarks>+    /// Default: EuclideanSq+    /// </remarks>+    void SetCellularReturnType(CellularReturnType cellularReturnType) { mCellularReturnType = cellularReturnType; }++    /// <summary>+    /// Sets the maximum distance a cellular point can move from it's grid position+    /// </summary>+    /// <remarks>+    /// Default: 1.0+    /// Note: Setting this higher than 1 will cause artifacts+    /// </remarks> +    void SetCellularJitter(float cellularJitter) { mCellularJitterModifier = cellularJitter; }+++    /// <summary>+    /// Sets the warp algorithm when using DomainWarp(...)+    /// </summary>+    /// <remarks>+    /// Default: OpenSimplex2+    /// </remarks>+    void SetDomainWarpType(DomainWarpType domainWarpType)+    {+        mDomainWarpType = domainWarpType;+        UpdateWarpTransformType3D();+    }+++    /// <summary>+    /// Sets the maximum warp distance from original position when using DomainWarp(...)+    /// </summary>+    /// <remarks>+    /// Default: 1.0+    /// </remarks>+    void SetDomainWarpAmp(float domainWarpAmp) { mDomainWarpAmp = domainWarpAmp; }+++    /// <summary>+    /// 2D noise at given position using current settings+    /// </summary>+    /// <returns>+    /// Noise output bounded between -1...1+    /// </returns>+    template <typename FNfloat>+    float GetNoise(FNfloat x, FNfloat y) const+    {+        Arguments_must_be_floating_point_values<FNfloat>();++        TransformNoiseCoordinate(x, y);++        switch (mFractalType)+        {+        default:+            return GenNoiseSingle(mSeed, x, y);+        case FractalType_FBm:+            return GenFractalFBm(x, y);+        case FractalType_Ridged:+            return GenFractalRidged(x, y);+        case FractalType_PingPong:+            return GenFractalPingPong(x, y);+        }+    }++    /// <summary>+    /// 3D noise at given position using current settings+    /// </summary>+    /// <returns>+    /// Noise output bounded between -1...1+    /// </returns>+    template <typename FNfloat>+    float GetNoise(FNfloat x, FNfloat y, FNfloat z) const+    {+        Arguments_must_be_floating_point_values<FNfloat>();++        TransformNoiseCoordinate(x, y, z);++        switch (mFractalType)+        {+        default:+            return GenNoiseSingle(mSeed, x, y, z);+        case FractalType_FBm:+            return GenFractalFBm(x, y, z);+        case FractalType_Ridged:+            return GenFractalRidged(x, y, z);+        case FractalType_PingPong:+            return GenFractalPingPong(x, y, z);+        }+    }+++    /// <summary>+    /// 2D warps the input position using current domain warp settings+    /// </summary>+    /// <example>+    /// Example usage with GetNoise+    /// <code>DomainWarp(x, y)+    /// noise = GetNoise(x, y)</code>+    /// </example>+    template <typename FNfloat>+    void DomainWarp(FNfloat& x, FNfloat& y) const+    {+        Arguments_must_be_floating_point_values<FNfloat>();++        switch (mFractalType)+        {+        default:+            DomainWarpSingle(x, y);+            break;+        case FractalType_DomainWarpProgressive:+            DomainWarpFractalProgressive(x, y);+            break;+        case FractalType_DomainWarpIndependent:+            DomainWarpFractalIndependent(x, y);+            break;+        }+    }++    /// <summary>+    /// 3D warps the input position using current domain warp settings+    /// </summary>+    /// <example>+    /// Example usage with GetNoise+    /// <code>DomainWarp(x, y, z)+    /// noise = GetNoise(x, y, z)</code>+    /// </example>+    template <typename FNfloat>+    void DomainWarp(FNfloat& x, FNfloat& y, FNfloat& z) const+    {+        Arguments_must_be_floating_point_values<FNfloat>();++        switch (mFractalType)+        {+        default:+            DomainWarpSingle(x, y, z);+            break;+        case FractalType_DomainWarpProgressive:+            DomainWarpFractalProgressive(x, y, z);+            break;+        case FractalType_DomainWarpIndependent:+            DomainWarpFractalIndependent(x, y, z);+            break;+        }+    }++private:+    template <typename T>+    struct Arguments_must_be_floating_point_values;++    enum TransformType3D+    {+        TransformType3D_None,+        TransformType3D_ImproveXYPlanes,+        TransformType3D_ImproveXZPlanes,+        TransformType3D_DefaultOpenSimplex2+    };++    int mSeed;+    float mFrequency;+    NoiseType mNoiseType;+    RotationType3D mRotationType3D;+    TransformType3D mTransformType3D;++    FractalType mFractalType;+    int mOctaves;+    float mLacunarity;+    float mGain;+    float mWeightedStrength;+    float mPingPongStrength;++    float mFractalBounding;++    CellularDistanceFunction mCellularDistanceFunction;+    CellularReturnType mCellularReturnType;+    float mCellularJitterModifier;++    DomainWarpType mDomainWarpType;+    TransformType3D mWarpTransformType3D;+    float mDomainWarpAmp;+++    template <typename T>+    struct Lookup+    {+        static const T Gradients2D[];+        static const T Gradients3D[];+        static const T RandVecs2D[];+        static const T RandVecs3D[];+    };++    static float FastMin(float a, float b) { return a < b ? a : b; }++    static float FastMax(float a, float b) { return a > b ? a : b; }++    static float FastAbs(float f) { return f < 0 ? -f : f; }++    static float FastSqrt(float f) { return sqrtf(f); }++    template <typename FNfloat>+    static int FastFloor(FNfloat f) { return f >= 0 ? (int)f : (int)f - 1; }++    template <typename FNfloat>+    static int FastRound(FNfloat f) { return f >= 0 ? (int)(f + 0.5f) : (int)(f - 0.5f); }++    static float Lerp(float a, float b, float t) { return a + t * (b - a); }++    static float InterpHermite(float t) { return t * t * (3 - 2 * t); }++    static float InterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); }++    static float CubicLerp(float a, float b, float c, float d, float t)+    {+        float p = (d - c) - (a - b);+        return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b;+    }++    static float PingPong(float t)+    {+        t -= (int)(t * 0.5f) * 2;+        return t < 1 ? t : 2 - t;+    }++    void CalculateFractalBounding()+    {+        float gain = FastAbs(mGain);+        float amp = gain;+        float ampFractal = 1.0f;+        for (int i = 1; i < mOctaves; i++)+        {+            ampFractal += amp;+            amp *= gain;+        }+        mFractalBounding = 1 / ampFractal;+    }++    // Hashing+    static const int PrimeX = 501125321;+    static const int PrimeY = 1136930381;+    static const int PrimeZ = 1720413743;++    static int Hash(int seed, int xPrimed, int yPrimed)+    {+        int hash = seed ^ xPrimed ^ yPrimed;++        hash *= 0x27d4eb2d;+        return hash;+    }+++    static int Hash(int seed, int xPrimed, int yPrimed, int zPrimed)+    {+        int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed;++        hash *= 0x27d4eb2d;+        return hash;+    }+++    static float ValCoord(int seed, int xPrimed, int yPrimed)+    {+        int hash = Hash(seed, xPrimed, yPrimed);++        hash *= hash;+        hash ^= hash << 19;+        return hash * (1 / 2147483648.0f);+    }+++    static float ValCoord(int seed, int xPrimed, int yPrimed, int zPrimed)+    {+        int hash = Hash(seed, xPrimed, yPrimed, zPrimed);++        hash *= hash;+        hash ^= hash << 19;+        return hash * (1 / 2147483648.0f);+    }+++    float GradCoord(int seed, int xPrimed, int yPrimed, float xd, float yd) const+    {+        int hash = Hash(seed, xPrimed, yPrimed);+        hash ^= hash >> 15;+        hash &= 127 << 1;++        float xg = Lookup<float>::Gradients2D[hash];+        float yg = Lookup<float>::Gradients2D[hash | 1];++        return xd * xg + yd * yg;+    }+++    float GradCoord(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd) const+    {+        int hash = Hash(seed, xPrimed, yPrimed, zPrimed);+        hash ^= hash >> 15;+        hash &= 63 << 2;++        float xg = Lookup<float>::Gradients3D[hash];+        float yg = Lookup<float>::Gradients3D[hash | 1];+        float zg = Lookup<float>::Gradients3D[hash | 2];++        return xd * xg + yd * yg + zd * zg;+    }+++    void GradCoordOut(int seed, int xPrimed, int yPrimed, float& xo, float& yo) const+    {+        int hash = Hash(seed, xPrimed, yPrimed) & (255 << 1);++        xo = Lookup<float>::RandVecs2D[hash];+        yo = Lookup<float>::RandVecs2D[hash | 1];+    }+++    void GradCoordOut(int seed, int xPrimed, int yPrimed, int zPrimed, float& xo, float& yo, float& zo) const+    {+        int hash = Hash(seed, xPrimed, yPrimed, zPrimed) & (255 << 2);++        xo = Lookup<float>::RandVecs3D[hash];+        yo = Lookup<float>::RandVecs3D[hash | 1];+        zo = Lookup<float>::RandVecs3D[hash | 2];+    }+++    void GradCoordDual(int seed, int xPrimed, int yPrimed, float xd, float yd, float& xo, float& yo) const+    {+        int hash = Hash(seed, xPrimed, yPrimed);+        int index1 = hash & (127 << 1);+        int index2 = (hash >> 7) & (255 << 1);++        float xg = Lookup<float>::Gradients2D[index1];+        float yg = Lookup<float>::Gradients2D[index1 | 1];+        float value = xd * xg + yd * yg;++        float xgo = Lookup<float>::RandVecs2D[index2];+        float ygo = Lookup<float>::RandVecs2D[index2 | 1];++        xo = value * xgo;+        yo = value * ygo;+    }+++    void GradCoordDual(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, float& xo, float& yo, float& zo) const+    {+        int hash = Hash(seed, xPrimed, yPrimed, zPrimed);+        int index1 = hash & (63 << 2);+        int index2 = (hash >> 6) & (255 << 2);++        float xg = Lookup<float>::Gradients3D[index1];+        float yg = Lookup<float>::Gradients3D[index1 | 1];+        float zg = Lookup<float>::Gradients3D[index1 | 2];+        float value = xd * xg + yd * yg + zd * zg;++        float xgo = Lookup<float>::RandVecs3D[index2];+        float ygo = Lookup<float>::RandVecs3D[index2 | 1];+        float zgo = Lookup<float>::RandVecs3D[index2 | 2];++        xo = value * xgo;+        yo = value * ygo;+        zo = value * zgo;+    }+++    // Generic noise gen++    template <typename FNfloat>+    float GenNoiseSingle(int seed, FNfloat x, FNfloat y) const+    {+        switch (mNoiseType)+        {+        case NoiseType_OpenSimplex2:+            return SingleSimplex(seed, x, y);+        case NoiseType_OpenSimplex2S:+            return SingleOpenSimplex2S(seed, x, y);+        case NoiseType_Cellular:+            return SingleCellular(seed, x, y);+        case NoiseType_Perlin:+            return SinglePerlin(seed, x, y);+        case NoiseType_ValueCubic:+            return SingleValueCubic(seed, x, y);+        case NoiseType_Value:+            return SingleValue(seed, x, y);+        default:+            return 0;+        }+    }++    template <typename FNfloat>+    float GenNoiseSingle(int seed, FNfloat x, FNfloat y, FNfloat z) const+    {+        switch (mNoiseType)+        {+        case NoiseType_OpenSimplex2:+            return SingleOpenSimplex2(seed, x, y, z);+        case NoiseType_OpenSimplex2S:+            return SingleOpenSimplex2S(seed, x, y, z);+        case NoiseType_Cellular:+            return SingleCellular(seed, x, y, z);+        case NoiseType_Perlin:+            return SinglePerlin(seed, x, y, z);+        case NoiseType_ValueCubic:+            return SingleValueCubic(seed, x, y, z);+        case NoiseType_Value:+            return SingleValue(seed, x, y, z);+        default:+            return 0;+        }+    }+++    // Noise Coordinate Transforms (frequency, and possible skew or rotation)++    template <typename FNfloat>+    void TransformNoiseCoordinate(FNfloat& x, FNfloat& y) const+    {+        x *= mFrequency;+        y *= mFrequency;++        switch (mNoiseType)+        {+        case NoiseType_OpenSimplex2:+        case NoiseType_OpenSimplex2S:+            {+                const FNfloat SQRT3 = (FNfloat)1.7320508075688772935274463415059;+                const FNfloat F2 = 0.5f * (SQRT3 - 1);+                FNfloat t = (x + y) * F2;+                x += t;+                y += t;+            }+            break;+        default:+            break;+        }+    }++    template <typename FNfloat>+    void TransformNoiseCoordinate(FNfloat& x, FNfloat& y, FNfloat& z) const+    {+        x *= mFrequency;+        y *= mFrequency;+        z *= mFrequency;++        switch (mTransformType3D)+        {+        case TransformType3D_ImproveXYPlanes:+            {+                FNfloat xy = x + y;+                FNfloat s2 = xy * -(FNfloat)0.211324865405187;+                z *= (FNfloat)0.577350269189626;+                x += s2 - z;+                y = y + s2 - z;+                z += xy * (FNfloat)0.577350269189626;+            }+            break;+        case TransformType3D_ImproveXZPlanes:+            {+                FNfloat xz = x + z;+                FNfloat s2 = xz * -(FNfloat)0.211324865405187;+                y *= (FNfloat)0.577350269189626;+                x += s2 - y;+                z += s2 - y;+                y += xz * (FNfloat)0.577350269189626;+            }+            break;+        case TransformType3D_DefaultOpenSimplex2:+            {+                const FNfloat R3 = (FNfloat)(2.0 / 3.0);+                FNfloat r = (x + y + z) * R3; // Rotation, not skew+                x = r - x;+                y = r - y;+                z = r - z;+            }+            break;+        default:+            break;+        }+    }++    void UpdateTransformType3D()+    {+        switch (mRotationType3D)+        {+        case RotationType3D_ImproveXYPlanes:+            mTransformType3D = TransformType3D_ImproveXYPlanes;+            break;+        case RotationType3D_ImproveXZPlanes:+            mTransformType3D = TransformType3D_ImproveXZPlanes;+            break;+        default:+            switch (mNoiseType)+            {+            case NoiseType_OpenSimplex2:+            case NoiseType_OpenSimplex2S:+                mTransformType3D = TransformType3D_DefaultOpenSimplex2;+                break;+            default:+                mTransformType3D = TransformType3D_None;+                break;+            }+            break;+        }+    }+++    // Domain Warp Coordinate Transforms++    template <typename FNfloat>+    void TransformDomainWarpCoordinate(FNfloat& x, FNfloat& y) const+    {+        switch (mDomainWarpType)+        {+        case DomainWarpType_OpenSimplex2:+        case DomainWarpType_OpenSimplex2Reduced:+            {+                const FNfloat SQRT3 = (FNfloat)1.7320508075688772935274463415059;+                const FNfloat F2 = 0.5f * (SQRT3 - 1);+                FNfloat t = (x + y) * F2;+                x += t;+                y += t;+            }+            break;+        default:+            break;+        }+    }++    template <typename FNfloat>+    void TransformDomainWarpCoordinate(FNfloat& x, FNfloat& y, FNfloat& z) const+    {+        switch (mWarpTransformType3D)+        {+        case TransformType3D_ImproveXYPlanes:+            {+                FNfloat xy = x + y;+                FNfloat s2 = xy * -(FNfloat)0.211324865405187;+                z *= (FNfloat)0.577350269189626;+                x += s2 - z;+                y = y + s2 - z;+                z += xy * (FNfloat)0.577350269189626;+            }+            break;+        case TransformType3D_ImproveXZPlanes:+            {+                FNfloat xz = x + z;+                FNfloat s2 = xz * -(FNfloat)0.211324865405187;+                y *= (FNfloat)0.577350269189626;+                x += s2 - y;+                z += s2 - y;+                y += xz * (FNfloat)0.577350269189626;+            }+            break;+        case TransformType3D_DefaultOpenSimplex2:+            {+                const FNfloat R3 = (FNfloat)(2.0 / 3.0);+                FNfloat r = (x + y + z) * R3; // Rotation, not skew+                x = r - x;+                y = r - y;+                z = r - z;+            }+            break;+        default:+            break;+        }+    }++    void UpdateWarpTransformType3D()+    {+        switch (mRotationType3D)+        {+        case RotationType3D_ImproveXYPlanes:+            mWarpTransformType3D = TransformType3D_ImproveXYPlanes;+            break;+        case RotationType3D_ImproveXZPlanes:+            mWarpTransformType3D = TransformType3D_ImproveXZPlanes;+            break;+        default:+            switch (mDomainWarpType)+            {+            case DomainWarpType_OpenSimplex2:+            case DomainWarpType_OpenSimplex2Reduced:+                mWarpTransformType3D = TransformType3D_DefaultOpenSimplex2;+                break;+            default:+                mWarpTransformType3D = TransformType3D_None;+                break;+            }+            break;+        }+    }+++    // Fractal FBm++    template <typename FNfloat>+    float GenFractalFBm(FNfloat x, FNfloat y) const+    {+        int seed = mSeed;+        float sum = 0;+        float amp = mFractalBounding;++        for (int i = 0; i < mOctaves; i++)+        {+            float noise = GenNoiseSingle(seed++, x, y);+            sum += noise * amp;+            amp *= Lerp(1.0f, FastMin(noise + 1, 2) * 0.5f, mWeightedStrength);++            x *= mLacunarity;+            y *= mLacunarity;+            amp *= mGain;+        }++        return sum;+    }++    template <typename FNfloat>+    float GenFractalFBm(FNfloat x, FNfloat y, FNfloat z) const+    {+        int seed = mSeed;+        float sum = 0;+        float amp = mFractalBounding;++        for (int i = 0; i < mOctaves; i++)+        {+            float noise = GenNoiseSingle(seed++, x, y, z);+            sum += noise * amp;+            amp *= Lerp(1.0f, (noise + 1) * 0.5f, mWeightedStrength);++            x *= mLacunarity;+            y *= mLacunarity;+            z *= mLacunarity;+            amp *= mGain;+        }++        return sum;+    }+++    // Fractal Ridged++    template <typename FNfloat>+    float GenFractalRidged(FNfloat x, FNfloat y) const+    {+        int seed = mSeed;+        float sum = 0;+        float amp = mFractalBounding;++        for (int i = 0; i < mOctaves; i++)+        {+            float noise = FastAbs(GenNoiseSingle(seed++, x, y));+            sum += (noise * -2 + 1) * amp;+            amp *= Lerp(1.0f, 1 - noise, mWeightedStrength);++            x *= mLacunarity;+            y *= mLacunarity;+            amp *= mGain;+        }++        return sum;+    }++    template <typename FNfloat>+    float GenFractalRidged(FNfloat x, FNfloat y, FNfloat z) const+    {+        int seed = mSeed;+        float sum = 0;+        float amp = mFractalBounding;++        for (int i = 0; i < mOctaves; i++)+        {+            float noise = FastAbs(GenNoiseSingle(seed++, x, y, z));+            sum += (noise * -2 + 1) * amp;+            amp *= Lerp(1.0f, 1 - noise, mWeightedStrength);++            x *= mLacunarity;+            y *= mLacunarity;+            z *= mLacunarity;+            amp *= mGain;+        }++        return sum;+    }+++    // Fractal PingPong ++    template <typename FNfloat>+    float GenFractalPingPong(FNfloat x, FNfloat y) const+    {+        int seed = mSeed;+        float sum = 0;+        float amp = mFractalBounding;++        for (int i = 0; i < mOctaves; i++)+        {+            float noise = PingPong((GenNoiseSingle(seed++, x, y) + 1) * mPingPongStrength);+            sum += (noise - 0.5f) * 2 * amp;+            amp *= Lerp(1.0f, noise, mWeightedStrength);++            x *= mLacunarity;+            y *= mLacunarity;+            amp *= mGain;+        }++        return sum;+    }++    template <typename FNfloat>+    float GenFractalPingPong(FNfloat x, FNfloat y, FNfloat z) const+    {+        int seed = mSeed;+        float sum = 0;+        float amp = mFractalBounding;++        for (int i = 0; i < mOctaves; i++)+        {+            float noise = PingPong((GenNoiseSingle(seed++, x, y, z) + 1) * mPingPongStrength);+            sum += (noise - 0.5f) * 2 * amp;+            amp *= Lerp(1.0f, noise, mWeightedStrength);++            x *= mLacunarity;+            y *= mLacunarity;+            z *= mLacunarity;+            amp *= mGain;+        }++        return sum;+    }+++    // Simplex/OpenSimplex2 Noise++    template <typename FNfloat>+    float SingleSimplex(int seed, FNfloat x, FNfloat y) const+    {+        // 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex.++        const float SQRT3 = 1.7320508075688772935274463415059f;+        const float G2 = (3 - SQRT3) / 6;++        /*+         * --- Skew moved to TransformNoiseCoordinate method ---+         * const FNfloat F2 = 0.5f * (SQRT3 - 1);+         * FNfloat s = (x + y) * F2;+         * x += s; y += s;+        */++        int i = FastFloor(x);+        int j = FastFloor(y);+        float xi = (float)(x - i);+        float yi = (float)(y - j);++        float t = (xi + yi) * G2;+        float x0 = (float)(xi - t);+        float y0 = (float)(yi - t);++        i *= PrimeX;+        j *= PrimeY;++        float n0, n1, n2;++        float a = 0.5f - x0 * x0 - y0 * y0;+        if (a <= 0) n0 = 0;+        else+        {+            n0 = (a * a) * (a * a) * GradCoord(seed, i, j, x0, y0);+        }++        float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a);+        if (c <= 0) n2 = 0;+        else+        {+            float x2 = x0 + (2 * (float)G2 - 1);+            float y2 = y0 + (2 * (float)G2 - 1);+            n2 = (c * c) * (c * c) * GradCoord(seed, i + PrimeX, j + PrimeY, x2, y2);+        }++        if (y0 > x0)+        {+            float x1 = x0 + (float)G2;+            float y1 = y0 + ((float)G2 - 1);+            float b = 0.5f - x1 * x1 - y1 * y1;+            if (b <= 0) n1 = 0;+            else+            {+                n1 = (b * b) * (b * b) * GradCoord(seed, i, j + PrimeY, x1, y1);+            }+        }+        else+        {+            float x1 = x0 + ((float)G2 - 1);+            float y1 = y0 + (float)G2;+            float b = 0.5f - x1 * x1 - y1 * y1;+            if (b <= 0) n1 = 0;+            else+            {+                n1 = (b * b) * (b * b) * GradCoord(seed, i + PrimeX, j, x1, y1);+            }+        }++        return (n0 + n1 + n2) * 99.83685446303647f;+    }++    template <typename FNfloat>+    float SingleOpenSimplex2(int seed, FNfloat x, FNfloat y, FNfloat z) const+    {+        // 3D OpenSimplex2 case uses two offset rotated cube grids.++        /*+         * --- Rotation moved to TransformNoiseCoordinate method ---+         * const FNfloat R3 = (FNfloat)(2.0 / 3.0);+         * FNfloat r = (x + y + z) * R3; // Rotation, not skew+         * x = r - x; y = r - y; z = r - z;+        */++        int i = FastRound(x);+        int j = FastRound(y);+        int k = FastRound(z);+        float x0 = (float)(x - i);+        float y0 = (float)(y - j);+        float z0 = (float)(z - k);++        int xNSign = (int)(-1.0f - x0) | 1;+        int yNSign = (int)(-1.0f - y0) | 1;+        int zNSign = (int)(-1.0f - z0) | 1;++        float ax0 = xNSign * -x0;+        float ay0 = yNSign * -y0;+        float az0 = zNSign * -z0;++        i *= PrimeX;+        j *= PrimeY;+        k *= PrimeZ;++        float value = 0;+        float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0);++        for (int l = 0; ; l++)+        {+            if (a > 0)+            {+                value += (a * a) * (a * a) * GradCoord(seed, i, j, k, x0, y0, z0);+            }++            float b = a + 1;+            int i1 = i;+            int j1 = j;+            int k1 = k;+            float x1 = x0;+            float y1 = y0;+            float z1 = z0;++            if (ax0 >= ay0 && ax0 >= az0)+            {+                x1 += xNSign;+                b -= xNSign * 2 * x1;+                i1 -= xNSign * PrimeX;+            }+            else if (ay0 > ax0 && ay0 >= az0)+            {+                y1 += yNSign;+                b -= yNSign * 2 * y1;+                j1 -= yNSign * PrimeY;+            }+            else+            {+                z1 += zNSign;+                b -= zNSign * 2 * z1;+                k1 -= zNSign * PrimeZ;+            }++            if (b > 0)+            {+                value += (b * b) * (b * b) * GradCoord(seed, i1, j1, k1, x1, y1, z1);+            }++            if (l == 1) break;++            ax0 = 0.5f - ax0;+            ay0 = 0.5f - ay0;+            az0 = 0.5f - az0;++            x0 = xNSign * ax0;+            y0 = yNSign * ay0;+            z0 = zNSign * az0;++            a += (0.75f - ax0) - (ay0 + az0);++            i += (xNSign >> 1) & PrimeX;+            j += (yNSign >> 1) & PrimeY;+            k += (zNSign >> 1) & PrimeZ;++            xNSign = -xNSign;+            yNSign = -yNSign;+            zNSign = -zNSign;++            seed = ~seed;+        }++        return value * 32.69428253173828125f;+    }+++    // OpenSimplex2S Noise++    template <typename FNfloat>+    float SingleOpenSimplex2S(int seed, FNfloat x, FNfloat y) const+    {+        // 2D OpenSimplex2S case is a modified 2D simplex noise.++        const FNfloat SQRT3 = (FNfloat)1.7320508075688772935274463415059;+        const FNfloat G2 = (3 - SQRT3) / 6;++        /*+         * --- Skew moved to TransformNoiseCoordinate method ---+         * const FNfloat F2 = 0.5f * (SQRT3 - 1);+         * FNfloat s = (x + y) * F2;+         * x += s; y += s;+        */++        int i = FastFloor(x);+        int j = FastFloor(y);+        float xi = (float)(x - i);+        float yi = (float)(y - j);++        i *= PrimeX;+        j *= PrimeY;+        int i1 = i + PrimeX;+        int j1 = j + PrimeY;++        float t = (xi + yi) * (float)G2;+        float x0 = xi - t;+        float y0 = yi - t;++        float a0 = (2.0f / 3.0f) - x0 * x0 - y0 * y0;+        float value = (a0 * a0) * (a0 * a0) * GradCoord(seed, i, j, x0, y0);++        float a1 = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a0);+        float x1 = x0 - (float)(1 - 2 * G2);+        float y1 = y0 - (float)(1 - 2 * G2);+        value += (a1 * a1) * (a1 * a1) * GradCoord(seed, i1, j1, x1, y1);++        // Nested conditionals were faster than compact bit logic/arithmetic.+        float xmyi = xi - yi;+        if (t > G2)+        {+            if (xi + xmyi > 1)+            {+                float x2 = x0 + (float)(3 * G2 - 2);+                float y2 = y0 + (float)(3 * G2 - 1);+                float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;+                if (a2 > 0)+                {+                    value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + (PrimeX << 1), j + PrimeY, x2, y2);+                }+            }+            else+            {+                float x2 = x0 + (float)G2;+                float y2 = y0 + (float)(G2 - 1);+                float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;+                if (a2 > 0)+                {+                    value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2);+                }+            }++            if (yi - xmyi > 1)+            {+                float x3 = x0 + (float)(3 * G2 - 1);+                float y3 = y0 + (float)(3 * G2 - 2);+                float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3;+                if (a3 > 0)+                {+                    value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j + (PrimeY << 1), x3, y3);+                }+            }+            else+            {+                float x3 = x0 + (float)(G2 - 1);+                float y3 = y0 + (float)G2;+                float a3 = (2.0f / 3.0f) - x3 * x3 - y3 * y3;+                if (a3 > 0)+                {+                    value += (a3 * a3) * (a3 * a3) * GradCoord(seed, i + PrimeX, j, x3, y3);+                }+            }+        }+        else+        {+            if (xi + xmyi < 0)+            {+                float x2 = x0 + (float)(1 - G2);+                float y2 = y0 - (float)G2;+                float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;+                if (a2 > 0)+                {+                    value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i - PrimeX, j, x2, y2);+                }+            }+            else+            {+                float x2 = x0 + (float)(G2 - 1);+                float y2 = y0 + (float)G2;+                float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;+                if (a2 > 0)+                {+                    value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i + PrimeX, j, x2, y2);+                }+            }++            if (yi < xmyi)+            {+                float x2 = x0 - (float)G2;+                float y2 = y0 - (float)(G2 - 1);+                float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;+                if (a2 > 0)+                {+                    value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j - PrimeY, x2, y2);+                }+            }+            else+            {+                float x2 = x0 + (float)G2;+                float y2 = y0 + (float)(G2 - 1);+                float a2 = (2.0f / 3.0f) - x2 * x2 - y2 * y2;+                if (a2 > 0)+                {+                    value += (a2 * a2) * (a2 * a2) * GradCoord(seed, i, j + PrimeY, x2, y2);+                }+            }+        }++        return value * 18.24196194486065f;+    }++    template <typename FNfloat>+    float SingleOpenSimplex2S(int seed, FNfloat x, FNfloat y, FNfloat z) const+    {+        // 3D OpenSimplex2S case uses two offset rotated cube grids.++        /*+         * --- Rotation moved to TransformNoiseCoordinate method ---+         * const FNfloat R3 = (FNfloat)(2.0 / 3.0);+         * FNfloat r = (x + y + z) * R3; // Rotation, not skew+         * x = r - x; y = r - y; z = r - z;+        */++        int i = FastFloor(x);+        int j = FastFloor(y);+        int k = FastFloor(z);+        float xi = (float)(x - i);+        float yi = (float)(y - j);+        float zi = (float)(z - k);++        i *= PrimeX;+        j *= PrimeY;+        k *= PrimeZ;+        int seed2 = seed + 1293373;++        int xNMask = (int)(-0.5f - xi);+        int yNMask = (int)(-0.5f - yi);+        int zNMask = (int)(-0.5f - zi);++        float x0 = xi + xNMask;+        float y0 = yi + yNMask;+        float z0 = zi + zNMask;+        float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0;+        float value = (a0 * a0) * (a0 * a0) * GradCoord(seed,+                                                        i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x0, y0, z0);++        float x1 = xi - 0.5f;+        float y1 = yi - 0.5f;+        float z1 = zi - 0.5f;+        float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1;+        value += (a1 * a1) * (a1 * a1) * GradCoord(seed2,+                                                   i + PrimeX, j + PrimeY, k + PrimeZ, x1, y1, z1);++        float xAFlipMask0 = ((xNMask | 1) << 1) * x1;+        float yAFlipMask0 = ((yNMask | 1) << 1) * y1;+        float zAFlipMask0 = ((zNMask | 1) << 1) * z1;+        float xAFlipMask1 = (-2 - (xNMask << 2)) * x1 - 1.0f;+        float yAFlipMask1 = (-2 - (yNMask << 2)) * y1 - 1.0f;+        float zAFlipMask1 = (-2 - (zNMask << 2)) * z1 - 1.0f;++        bool skip5 = false;+        float a2 = xAFlipMask0 + a0;+        if (a2 > 0)+        {+            float x2 = x0 - (xNMask | 1);+            float y2 = y0;+            float z2 = z0;+            value += (a2 * a2) * (a2 * a2) * GradCoord(seed,+                                                       i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (zNMask & PrimeZ), x2, y2, z2);+        }+        else+        {+            float a3 = yAFlipMask0 + zAFlipMask0 + a0;+            if (a3 > 0)+            {+                float x3 = x0;+                float y3 = y0 - (yNMask | 1);+                float z3 = z0 - (zNMask | 1);+                value += (a3 * a3) * (a3 * a3) * GradCoord(seed,+                                                           i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (~zNMask & PrimeZ), x3, y3, z3);+            }++            float a4 = xAFlipMask1 + a1;+            if (a4 > 0)+            {+                float x4 = (xNMask | 1) + x1;+                float y4 = y1;+                float z4 = z1;+                value += (a4 * a4) * (a4 * a4) * GradCoord(seed2,+                                                           i + (xNMask & (PrimeX * 2)), j + PrimeY, k + PrimeZ, x4, y4, z4);+                skip5 = true;+            }+        }++        bool skip9 = false;+        float a6 = yAFlipMask0 + a0;+        if (a6 > 0)+        {+            float x6 = x0;+            float y6 = y0 - (yNMask | 1);+            float z6 = z0;+            value += (a6 * a6) * (a6 * a6) * GradCoord(seed,+                                                       i + (xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), x6, y6, z6);+        }+        else+        {+            float a7 = xAFlipMask0 + zAFlipMask0 + a0;+            if (a7 > 0)+            {+                float x7 = x0 - (xNMask | 1);+                float y7 = y0;+                float z7 = z0 - (zNMask | 1);+                value += (a7 * a7) * (a7 * a7) * GradCoord(seed,+                                                           i + (~xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), x7, y7, z7);+            }++            float a8 = yAFlipMask1 + a1;+            if (a8 > 0)+            {+                float x8 = x1;+                float y8 = (yNMask | 1) + y1;+                float z8 = z1;+                value += (a8 * a8) * (a8 * a8) * GradCoord(seed2,+                                                           i + PrimeX, j + (yNMask & (PrimeY << 1)), k + PrimeZ, x8, y8, z8);+                skip9 = true;+            }+        }++        bool skipD = false;+        float aA = zAFlipMask0 + a0;+        if (aA > 0)+        {+            float xA = x0;+            float yA = y0;+            float zA = z0 - (zNMask | 1);+            value += (aA * aA) * (aA * aA) * GradCoord(seed,+                                                       i + (xNMask & PrimeX), j + (yNMask & PrimeY), k + (~zNMask & PrimeZ), xA, yA, zA);+        }+        else+        {+            float aB = xAFlipMask0 + yAFlipMask0 + a0;+            if (aB > 0)+            {+                float xB = x0 - (xNMask | 1);+                float yB = y0 - (yNMask | 1);+                float zB = z0;+                value += (aB * aB) * (aB * aB) * GradCoord(seed,+                                                           i + (~xNMask & PrimeX), j + (~yNMask & PrimeY), k + (zNMask & PrimeZ), xB, yB, zB);+            }++            float aC = zAFlipMask1 + a1;+            if (aC > 0)+            {+                float xC = x1;+                float yC = y1;+                float zC = (zNMask | 1) + z1;+                value += (aC * aC) * (aC * aC) * GradCoord(seed2,+                                                           i + PrimeX, j + PrimeY, k + (zNMask & (PrimeZ << 1)), xC, yC, zC);+                skipD = true;+            }+        }++        if (!skip5)+        {+            float a5 = yAFlipMask1 + zAFlipMask1 + a1;+            if (a5 > 0)+            {+                float x5 = x1;+                float y5 = (yNMask | 1) + y1;+                float z5 = (zNMask | 1) + z1;+                value += (a5 * a5) * (a5 * a5) * GradCoord(seed2,+                                                           i + PrimeX, j + (yNMask & (PrimeY << 1)), k + (zNMask & (PrimeZ << 1)), x5, y5, z5);+            }+        }++        if (!skip9)+        {+            float a9 = xAFlipMask1 + zAFlipMask1 + a1;+            if (a9 > 0)+            {+                float x9 = (xNMask | 1) + x1;+                float y9 = y1;+                float z9 = (zNMask | 1) + z1;+                value += (a9 * a9) * (a9 * a9) * GradCoord(seed2,+                                                           i + (xNMask & (PrimeX * 2)), j + PrimeY, k + (zNMask & (PrimeZ << 1)), x9, y9, z9);+            }+        }++        if (!skipD)+        {+            float aD = xAFlipMask1 + yAFlipMask1 + a1;+            if (aD > 0)+            {+                float xD = (xNMask | 1) + x1;+                float yD = (yNMask | 1) + y1;+                float zD = z1;+                value += (aD * aD) * (aD * aD) * GradCoord(seed2,+                                                           i + (xNMask & (PrimeX << 1)), j + (yNMask & (PrimeY << 1)), k + PrimeZ, xD, yD, zD);+            }+        }++        return value * 9.046026385208288f;+    }+++    // Cellular Noise++    template <typename FNfloat>+    float SingleCellular(int seed, FNfloat x, FNfloat y) const+    {+        int xr = FastRound(x);+        int yr = FastRound(y);++        float distance0 = 1e10f;+        float distance1 = 1e10f;+        int closestHash = 0;++        float cellularJitter = 0.43701595f * mCellularJitterModifier;++        int xPrimed = (xr - 1) * PrimeX;+        int yPrimedBase = (yr - 1) * PrimeY;++        switch (mCellularDistanceFunction)+        {+        default:+        case CellularDistanceFunction_Euclidean:+        case CellularDistanceFunction_EuclideanSq:+            for (int xi = xr - 1; xi <= xr + 1; xi++)+            {+                int yPrimed = yPrimedBase;++                for (int yi = yr - 1; yi <= yr + 1; yi++)+                {+                    int hash = Hash(seed, xPrimed, yPrimed);+                    int idx = hash & (255 << 1);++                    float vecX = (float)(xi - x) + Lookup<float>::RandVecs2D[idx] * cellularJitter;+                    float vecY = (float)(yi - y) + Lookup<float>::RandVecs2D[idx | 1] * cellularJitter;++                    float newDistance = vecX * vecX + vecY * vecY;++                    distance1 = FastMax(FastMin(distance1, newDistance), distance0);+                    if (newDistance < distance0)+                    {+                        distance0 = newDistance;+                        closestHash = hash;+                    }+                    yPrimed += PrimeY;+                }+                xPrimed += PrimeX;+            }+            break;+        case CellularDistanceFunction_Manhattan:+            for (int xi = xr - 1; xi <= xr + 1; xi++)+            {+                int yPrimed = yPrimedBase;++                for (int yi = yr - 1; yi <= yr + 1; yi++)+                {+                    int hash = Hash(seed, xPrimed, yPrimed);+                    int idx = hash & (255 << 1);++                    float vecX = (float)(xi - x) + Lookup<float>::RandVecs2D[idx] * cellularJitter;+                    float vecY = (float)(yi - y) + Lookup<float>::RandVecs2D[idx | 1] * cellularJitter;++                    float newDistance = FastAbs(vecX) + FastAbs(vecY);++                    distance1 = FastMax(FastMin(distance1, newDistance), distance0);+                    if (newDistance < distance0)+                    {+                        distance0 = newDistance;+                        closestHash = hash;+                    }+                    yPrimed += PrimeY;+                }+                xPrimed += PrimeX;+            }+            break;+        case CellularDistanceFunction_Hybrid:+            for (int xi = xr - 1; xi <= xr + 1; xi++)+            {+                int yPrimed = yPrimedBase;++                for (int yi = yr - 1; yi <= yr + 1; yi++)+                {+                    int hash = Hash(seed, xPrimed, yPrimed);+                    int idx = hash & (255 << 1);++                    float vecX = (float)(xi - x) + Lookup<float>::RandVecs2D[idx] * cellularJitter;+                    float vecY = (float)(yi - y) + Lookup<float>::RandVecs2D[idx | 1] * cellularJitter;++                    float newDistance = (FastAbs(vecX) + FastAbs(vecY)) + (vecX * vecX + vecY * vecY);++                    distance1 = FastMax(FastMin(distance1, newDistance), distance0);+                    if (newDistance < distance0)+                    {+                        distance0 = newDistance;+                        closestHash = hash;+                    }+                    yPrimed += PrimeY;+                }+                xPrimed += PrimeX;+            }+            break;+        }++        if (mCellularDistanceFunction == CellularDistanceFunction_Euclidean && mCellularReturnType >= CellularReturnType_Distance)+        {+            distance0 = FastSqrt(distance0);++            if (mCellularReturnType >= CellularReturnType_Distance2)+            {+                distance1 = FastSqrt(distance1);+            }+        }++        switch (mCellularReturnType)+        {+        case CellularReturnType_CellValue:+            return closestHash * (1 / 2147483648.0f);+        case CellularReturnType_Distance:+            return distance0 - 1;+        case CellularReturnType_Distance2:+            return distance1 - 1;+        case CellularReturnType_Distance2Add:+            return (distance1 + distance0) * 0.5f - 1;+        case CellularReturnType_Distance2Sub:+            return distance1 - distance0 - 1;+        case CellularReturnType_Distance2Mul:+            return distance1 * distance0 * 0.5f - 1;+        case CellularReturnType_Distance2Div:+            return distance0 / distance1 - 1;+        default:+            return 0;+        }+    }++    template <typename FNfloat>+    float SingleCellular(int seed, FNfloat x, FNfloat y, FNfloat z) const+    {+        int xr = FastRound(x);+        int yr = FastRound(y);+        int zr = FastRound(z);++        float distance0 = 1e10f;+        float distance1 = 1e10f;+        int closestHash = 0;++        float cellularJitter = 0.39614353f * mCellularJitterModifier;++        int xPrimed = (xr - 1) * PrimeX;+        int yPrimedBase = (yr - 1) * PrimeY;+        int zPrimedBase = (zr - 1) * PrimeZ;++        switch (mCellularDistanceFunction)+        {+        case CellularDistanceFunction_Euclidean:+        case CellularDistanceFunction_EuclideanSq:+            for (int xi = xr - 1; xi <= xr + 1; xi++)+            {+                int yPrimed = yPrimedBase;++                for (int yi = yr - 1; yi <= yr + 1; yi++)+                {+                    int zPrimed = zPrimedBase;++                    for (int zi = zr - 1; zi <= zr + 1; zi++)+                    {+                        int hash = Hash(seed, xPrimed, yPrimed, zPrimed);+                        int idx = hash & (255 << 2);++                        float vecX = (float)(xi - x) + Lookup<float>::RandVecs3D[idx] * cellularJitter;+                        float vecY = (float)(yi - y) + Lookup<float>::RandVecs3D[idx | 1] * cellularJitter;+                        float vecZ = (float)(zi - z) + Lookup<float>::RandVecs3D[idx | 2] * cellularJitter;++                        float newDistance = vecX * vecX + vecY * vecY + vecZ * vecZ;++                        distance1 = FastMax(FastMin(distance1, newDistance), distance0);+                        if (newDistance < distance0)+                        {+                            distance0 = newDistance;+                            closestHash = hash;+                        }+                        zPrimed += PrimeZ;+                    }+                    yPrimed += PrimeY;+                }+                xPrimed += PrimeX;+            }+            break;+        case CellularDistanceFunction_Manhattan:+            for (int xi = xr - 1; xi <= xr + 1; xi++)+            {+                int yPrimed = yPrimedBase;++                for (int yi = yr - 1; yi <= yr + 1; yi++)+                {+                    int zPrimed = zPrimedBase;++                    for (int zi = zr - 1; zi <= zr + 1; zi++)+                    {+                        int hash = Hash(seed, xPrimed, yPrimed, zPrimed);+                        int idx = hash & (255 << 2);++                        float vecX = (float)(xi - x) + Lookup<float>::RandVecs3D[idx] * cellularJitter;+                        float vecY = (float)(yi - y) + Lookup<float>::RandVecs3D[idx | 1] * cellularJitter;+                        float vecZ = (float)(zi - z) + Lookup<float>::RandVecs3D[idx | 2] * cellularJitter;++                        float newDistance = FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ);++                        distance1 = FastMax(FastMin(distance1, newDistance), distance0);+                        if (newDistance < distance0)+                        {+                            distance0 = newDistance;+                            closestHash = hash;+                        }+                        zPrimed += PrimeZ;+                    }+                    yPrimed += PrimeY;+                }+                xPrimed += PrimeX;+            }+            break;+        case CellularDistanceFunction_Hybrid:+            for (int xi = xr - 1; xi <= xr + 1; xi++)+            {+                int yPrimed = yPrimedBase;++                for (int yi = yr - 1; yi <= yr + 1; yi++)+                {+                    int zPrimed = zPrimedBase;++                    for (int zi = zr - 1; zi <= zr + 1; zi++)+                    {+                        int hash = Hash(seed, xPrimed, yPrimed, zPrimed);+                        int idx = hash & (255 << 2);++                        float vecX = (float)(xi - x) + Lookup<float>::RandVecs3D[idx] * cellularJitter;+                        float vecY = (float)(yi - y) + Lookup<float>::RandVecs3D[idx | 1] * cellularJitter;+                        float vecZ = (float)(zi - z) + Lookup<float>::RandVecs3D[idx | 2] * cellularJitter;++                        float newDistance = (FastAbs(vecX) + FastAbs(vecY) + FastAbs(vecZ)) + (vecX * vecX + vecY * vecY + vecZ * vecZ);++                        distance1 = FastMax(FastMin(distance1, newDistance), distance0);+                        if (newDistance < distance0)+                        {+                            distance0 = newDistance;+                            closestHash = hash;+                        }+                        zPrimed += PrimeZ;+                    }+                    yPrimed += PrimeY;+                }+                xPrimed += PrimeX;+            }+            break;+        default:+            break;+        }++        if (mCellularDistanceFunction == CellularDistanceFunction_Euclidean && mCellularReturnType >= CellularReturnType_Distance)+        {+            distance0 = FastSqrt(distance0);++            if (mCellularReturnType >= CellularReturnType_Distance2)+            {+                distance1 = FastSqrt(distance1);+            }+        }++        switch (mCellularReturnType)+        {+        case CellularReturnType_CellValue:+            return closestHash * (1 / 2147483648.0f);+        case CellularReturnType_Distance:+            return distance0 - 1;+        case CellularReturnType_Distance2:+            return distance1 - 1;+        case CellularReturnType_Distance2Add:+            return (distance1 + distance0) * 0.5f - 1;+        case CellularReturnType_Distance2Sub:+            return distance1 - distance0 - 1;+        case CellularReturnType_Distance2Mul:+            return distance1 * distance0 * 0.5f - 1;+        case CellularReturnType_Distance2Div:+            return distance0 / distance1 - 1;+        default:+            return 0;+        }+    }+++    // Perlin Noise++    template <typename FNfloat>+    float SinglePerlin(int seed, FNfloat x, FNfloat y) const+    {+        int x0 = FastFloor(x);+        int y0 = FastFloor(y);++        float xd0 = (float)(x - x0);+        float yd0 = (float)(y - y0);+        float xd1 = xd0 - 1;+        float yd1 = yd0 - 1;++        float xs = InterpQuintic(xd0);+        float ys = InterpQuintic(yd0);++        x0 *= PrimeX;+        y0 *= PrimeY;+        int x1 = x0 + PrimeX;+        int y1 = y0 + PrimeY;++        float xf0 = Lerp(GradCoord(seed, x0, y0, xd0, yd0), GradCoord(seed, x1, y0, xd1, yd0), xs);+        float xf1 = Lerp(GradCoord(seed, x0, y1, xd0, yd1), GradCoord(seed, x1, y1, xd1, yd1), xs);++        return Lerp(xf0, xf1, ys) * 1.4247691104677813f;+    }++    template <typename FNfloat>+    float SinglePerlin(int seed, FNfloat x, FNfloat y, FNfloat z) const+    {+        int x0 = FastFloor(x);+        int y0 = FastFloor(y);+        int z0 = FastFloor(z);++        float xd0 = (float)(x - x0);+        float yd0 = (float)(y - y0);+        float zd0 = (float)(z - z0);+        float xd1 = xd0 - 1;+        float yd1 = yd0 - 1;+        float zd1 = zd0 - 1;++        float xs = InterpQuintic(xd0);+        float ys = InterpQuintic(yd0);+        float zs = InterpQuintic(zd0);++        x0 *= PrimeX;+        y0 *= PrimeY;+        z0 *= PrimeZ;+        int x1 = x0 + PrimeX;+        int y1 = y0 + PrimeY;+        int z1 = z0 + PrimeZ;++        float xf00 = Lerp(GradCoord(seed, x0, y0, z0, xd0, yd0, zd0), GradCoord(seed, x1, y0, z0, xd1, yd0, zd0), xs);+        float xf10 = Lerp(GradCoord(seed, x0, y1, z0, xd0, yd1, zd0), GradCoord(seed, x1, y1, z0, xd1, yd1, zd0), xs);+        float xf01 = Lerp(GradCoord(seed, x0, y0, z1, xd0, yd0, zd1), GradCoord(seed, x1, y0, z1, xd1, yd0, zd1), xs);+        float xf11 = Lerp(GradCoord(seed, x0, y1, z1, xd0, yd1, zd1), GradCoord(seed, x1, y1, z1, xd1, yd1, zd1), xs);++        float yf0 = Lerp(xf00, xf10, ys);+        float yf1 = Lerp(xf01, xf11, ys);++        return Lerp(yf0, yf1, zs) * 0.964921414852142333984375f;+    }+++    // Value Cubic Noise++    template <typename FNfloat>+    float SingleValueCubic(int seed, FNfloat x, FNfloat y) const+    {+        int x1 = FastFloor(x);+        int y1 = FastFloor(y);++        float xs = (float)(x - x1);+        float ys = (float)(y - y1);++        x1 *= PrimeX;+        y1 *= PrimeY;+        int x0 = x1 - PrimeX;+        int y0 = y1 - PrimeY;+        int x2 = x1 + PrimeX;+        int y2 = y1 + PrimeY;+        int x3 = x1 + (int)((long)PrimeX << 1);+        int y3 = y1 + (int)((long)PrimeY << 1);++        return CubicLerp(+            CubicLerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), ValCoord(seed, x2, y0), ValCoord(seed, x3, y0),+                      xs),+            CubicLerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), ValCoord(seed, x2, y1), ValCoord(seed, x3, y1),+                      xs),+            CubicLerp(ValCoord(seed, x0, y2), ValCoord(seed, x1, y2), ValCoord(seed, x2, y2), ValCoord(seed, x3, y2),+                      xs),+            CubicLerp(ValCoord(seed, x0, y3), ValCoord(seed, x1, y3), ValCoord(seed, x2, y3), ValCoord(seed, x3, y3),+                      xs),+            ys) * (1 / (1.5f * 1.5f));+    }++    template <typename FNfloat>+    float SingleValueCubic(int seed, FNfloat x, FNfloat y, FNfloat z) const+    {+        int x1 = FastFloor(x);+        int y1 = FastFloor(y);+        int z1 = FastFloor(z);++        float xs = (float)(x - x1);+        float ys = (float)(y - y1);+        float zs = (float)(z - z1);++        x1 *= PrimeX;+        y1 *= PrimeY;+        z1 *= PrimeZ;++        int x0 = x1 - PrimeX;+        int y0 = y1 - PrimeY;+        int z0 = z1 - PrimeZ;+        int x2 = x1 + PrimeX;+        int y2 = y1 + PrimeY;+        int z2 = z1 + PrimeZ;+        int x3 = x1 + (int)((long)PrimeX << 1);+        int y3 = y1 + (int)((long)PrimeY << 1);+        int z3 = z1 + (int)((long)PrimeZ << 1);+++        return CubicLerp(+            CubicLerp(+                CubicLerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), ValCoord(seed, x2, y0, z0), ValCoord(seed, x3, y0, z0), xs),+                CubicLerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), ValCoord(seed, x2, y1, z0), ValCoord(seed, x3, y1, z0), xs),+                CubicLerp(ValCoord(seed, x0, y2, z0), ValCoord(seed, x1, y2, z0), ValCoord(seed, x2, y2, z0), ValCoord(seed, x3, y2, z0), xs),+                CubicLerp(ValCoord(seed, x0, y3, z0), ValCoord(seed, x1, y3, z0), ValCoord(seed, x2, y3, z0), ValCoord(seed, x3, y3, z0), xs),+                ys),+            CubicLerp(+                CubicLerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), ValCoord(seed, x2, y0, z1), ValCoord(seed, x3, y0, z1), xs),+                CubicLerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), ValCoord(seed, x2, y1, z1), ValCoord(seed, x3, y1, z1), xs),+                CubicLerp(ValCoord(seed, x0, y2, z1), ValCoord(seed, x1, y2, z1), ValCoord(seed, x2, y2, z1), ValCoord(seed, x3, y2, z1), xs),+                CubicLerp(ValCoord(seed, x0, y3, z1), ValCoord(seed, x1, y3, z1), ValCoord(seed, x2, y3, z1), ValCoord(seed, x3, y3, z1), xs),+                ys),+            CubicLerp(+                CubicLerp(ValCoord(seed, x0, y0, z2), ValCoord(seed, x1, y0, z2), ValCoord(seed, x2, y0, z2), ValCoord(seed, x3, y0, z2), xs),+                CubicLerp(ValCoord(seed, x0, y1, z2), ValCoord(seed, x1, y1, z2), ValCoord(seed, x2, y1, z2), ValCoord(seed, x3, y1, z2), xs),+                CubicLerp(ValCoord(seed, x0, y2, z2), ValCoord(seed, x1, y2, z2), ValCoord(seed, x2, y2, z2), ValCoord(seed, x3, y2, z2), xs),+                CubicLerp(ValCoord(seed, x0, y3, z2), ValCoord(seed, x1, y3, z2), ValCoord(seed, x2, y3, z2), ValCoord(seed, x3, y3, z2), xs),+                ys),+            CubicLerp(+                CubicLerp(ValCoord(seed, x0, y0, z3), ValCoord(seed, x1, y0, z3), ValCoord(seed, x2, y0, z3), ValCoord(seed, x3, y0, z3), xs),+                CubicLerp(ValCoord(seed, x0, y1, z3), ValCoord(seed, x1, y1, z3), ValCoord(seed, x2, y1, z3), ValCoord(seed, x3, y1, z3), xs),+                CubicLerp(ValCoord(seed, x0, y2, z3), ValCoord(seed, x1, y2, z3), ValCoord(seed, x2, y2, z3), ValCoord(seed, x3, y2, z3), xs),+                CubicLerp(ValCoord(seed, x0, y3, z3), ValCoord(seed, x1, y3, z3), ValCoord(seed, x2, y3, z3), ValCoord(seed, x3, y3, z3), xs),+                ys),+            zs) * (1 / (1.5f * 1.5f * 1.5f));+    }+++    // Value Noise++    template <typename FNfloat>+    float SingleValue(int seed, FNfloat x, FNfloat y) const+    {+        int x0 = FastFloor(x);+        int y0 = FastFloor(y);++        float xs = InterpHermite((float)(x - x0));+        float ys = InterpHermite((float)(y - y0));++        x0 *= PrimeX;+        y0 *= PrimeY;+        int x1 = x0 + PrimeX;+        int y1 = y0 + PrimeY;++        float xf0 = Lerp(ValCoord(seed, x0, y0), ValCoord(seed, x1, y0), xs);+        float xf1 = Lerp(ValCoord(seed, x0, y1), ValCoord(seed, x1, y1), xs);++        return Lerp(xf0, xf1, ys);+    }++    template <typename FNfloat>+    float SingleValue(int seed, FNfloat x, FNfloat y, FNfloat z) const+    {+        int x0 = FastFloor(x);+        int y0 = FastFloor(y);+        int z0 = FastFloor(z);++        float xs = InterpHermite((float)(x - x0));+        float ys = InterpHermite((float)(y - y0));+        float zs = InterpHermite((float)(z - z0));++        x0 *= PrimeX;+        y0 *= PrimeY;+        z0 *= PrimeZ;+        int x1 = x0 + PrimeX;+        int y1 = y0 + PrimeY;+        int z1 = z0 + PrimeZ;++        float xf00 = Lerp(ValCoord(seed, x0, y0, z0), ValCoord(seed, x1, y0, z0), xs);+        float xf10 = Lerp(ValCoord(seed, x0, y1, z0), ValCoord(seed, x1, y1, z0), xs);+        float xf01 = Lerp(ValCoord(seed, x0, y0, z1), ValCoord(seed, x1, y0, z1), xs);+        float xf11 = Lerp(ValCoord(seed, x0, y1, z1), ValCoord(seed, x1, y1, z1), xs);++        float yf0 = Lerp(xf00, xf10, ys);+        float yf1 = Lerp(xf01, xf11, ys);++        return Lerp(yf0, yf1, zs);+    }+++    // Domain Warp++    template <typename FNfloat>+    void DoSingleDomainWarp(int seed, float amp, float freq, FNfloat x, FNfloat y, FNfloat& xr, FNfloat& yr) const+    {+        switch (mDomainWarpType)+        {+        case DomainWarpType_OpenSimplex2:+            SingleDomainWarpSimplexGradient(seed, amp * 38.283687591552734375f, freq, x, y, xr, yr, false);+            break;+        case DomainWarpType_OpenSimplex2Reduced:+            SingleDomainWarpSimplexGradient(seed, amp * 16.0f, freq, x, y, xr, yr, true);+            break;+        case DomainWarpType_BasicGrid:+            SingleDomainWarpBasicGrid(seed, amp, freq, x, y, xr, yr);+            break;+        }+    }++    template <typename FNfloat>+    void DoSingleDomainWarp(int seed, float amp, float freq, FNfloat x, FNfloat y, FNfloat z, FNfloat& xr, FNfloat& yr, FNfloat& zr) const+    {+        switch (mDomainWarpType)+        {+        case DomainWarpType_OpenSimplex2:+            SingleDomainWarpOpenSimplex2Gradient(seed, amp * 32.69428253173828125f, freq, x, y, z, xr, yr, zr, false);+            break;+        case DomainWarpType_OpenSimplex2Reduced:+            SingleDomainWarpOpenSimplex2Gradient(seed, amp * 7.71604938271605f, freq, x, y, z, xr, yr, zr, true);+            break;+        case DomainWarpType_BasicGrid:+            SingleDomainWarpBasicGrid(seed, amp, freq, x, y, z, xr, yr, zr);+            break;+        }+    }+++    // Domain Warp Single Wrapper++    template <typename FNfloat>+    void DomainWarpSingle(FNfloat& x, FNfloat& y) const+    {+        int seed = mSeed;+        float amp = mDomainWarpAmp * mFractalBounding;+        float freq = mFrequency;++        FNfloat xs = x;+        FNfloat ys = y;+        TransformDomainWarpCoordinate(xs, ys);++        DoSingleDomainWarp(seed, amp, freq, xs, ys, x, y);+    }++    template <typename FNfloat>+    void DomainWarpSingle(FNfloat& x, FNfloat& y, FNfloat& z) const+    {+        int seed = mSeed;+        float amp = mDomainWarpAmp * mFractalBounding;+        float freq = mFrequency;++        FNfloat xs = x;+        FNfloat ys = y;+        FNfloat zs = z;+        TransformDomainWarpCoordinate(xs, ys, zs);++        DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, x, y, z);+    }+++    // Domain Warp Fractal Progressive++    template <typename FNfloat>+    void DomainWarpFractalProgressive(FNfloat& x, FNfloat& y) const+    {+        int seed = mSeed;+        float amp = mDomainWarpAmp * mFractalBounding;+        float freq = mFrequency;++        for (int i = 0; i < mOctaves; i++)+        {+            FNfloat xs = x;+            FNfloat ys = y;+            TransformDomainWarpCoordinate(xs, ys);++            DoSingleDomainWarp(seed, amp, freq, xs, ys, x, y);++            seed++;+            amp *= mGain;+            freq *= mLacunarity;+        }+    }++    template <typename FNfloat>+    void DomainWarpFractalProgressive(FNfloat& x, FNfloat& y, FNfloat& z) const+    {+        int seed = mSeed;+        float amp = mDomainWarpAmp * mFractalBounding;+        float freq = mFrequency;++        for (int i = 0; i < mOctaves; i++)+        {+            FNfloat xs = x;+            FNfloat ys = y;+            FNfloat zs = z;+            TransformDomainWarpCoordinate(xs, ys, zs);++            DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, x, y, z);++            seed++;+            amp *= mGain;+            freq *= mLacunarity;+        }+    }+++    // Domain Warp Fractal Independant++    template <typename FNfloat>+    void DomainWarpFractalIndependent(FNfloat& x, FNfloat& y) const+    {+        FNfloat xs = x;+        FNfloat ys = y;+        TransformDomainWarpCoordinate(xs, ys);++        int seed = mSeed;+        float amp = mDomainWarpAmp * mFractalBounding;+        float freq = mFrequency;++        for (int i = 0; i < mOctaves; i++)+        {+            DoSingleDomainWarp(seed, amp, freq, xs, ys, x, y);++            seed++;+            amp *= mGain;+            freq *= mLacunarity;+        }+    }++    template <typename FNfloat>+    void DomainWarpFractalIndependent(FNfloat& x, FNfloat& y, FNfloat& z) const+    {+        FNfloat xs = x;+        FNfloat ys = y;+        FNfloat zs = z;+        TransformDomainWarpCoordinate(xs, ys, zs);++        int seed = mSeed;+        float amp = mDomainWarpAmp * mFractalBounding;+        float freq = mFrequency;++        for (int i = 0; i < mOctaves; i++)+        {+            DoSingleDomainWarp(seed, amp, freq, xs, ys, zs, x, y, z);++            seed++;+            amp *= mGain;+            freq *= mLacunarity;+        }+    }+++    // Domain Warp Basic Grid++    template <typename FNfloat>+    void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat& xr, FNfloat& yr) const+    {+        FNfloat xf = x * frequency;+        FNfloat yf = y * frequency;++        int x0 = FastFloor(xf);+        int y0 = FastFloor(yf);++        float xs = InterpHermite((float)(xf - x0));+        float ys = InterpHermite((float)(yf - y0));++        x0 *= PrimeX;+        y0 *= PrimeY;+        int x1 = x0 + PrimeX;+        int y1 = y0 + PrimeY;++        int hash0 = Hash(seed, x0, y0) & (255 << 1);+        int hash1 = Hash(seed, x1, y0) & (255 << 1);++        float lx0x = Lerp(Lookup<float>::RandVecs2D[hash0], Lookup<float>::RandVecs2D[hash1], xs);+        float ly0x = Lerp(Lookup<float>::RandVecs2D[hash0 | 1], Lookup<float>::RandVecs2D[hash1 | 1], xs);++        hash0 = Hash(seed, x0, y1) & (255 << 1);+        hash1 = Hash(seed, x1, y1) & (255 << 1);++        float lx1x = Lerp(Lookup<float>::RandVecs2D[hash0], Lookup<float>::RandVecs2D[hash1], xs);+        float ly1x = Lerp(Lookup<float>::RandVecs2D[hash0 | 1], Lookup<float>::RandVecs2D[hash1 | 1], xs);++        xr += Lerp(lx0x, lx1x, ys) * warpAmp;+        yr += Lerp(ly0x, ly1x, ys) * warpAmp;+    }++    template <typename FNfloat>+    void SingleDomainWarpBasicGrid(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat z, FNfloat& xr, FNfloat& yr, FNfloat& zr) const+    {+        FNfloat xf = x * frequency;+        FNfloat yf = y * frequency;+        FNfloat zf = z * frequency;++        int x0 = FastFloor(xf);+        int y0 = FastFloor(yf);+        int z0 = FastFloor(zf);++        float xs = InterpHermite((float)(xf - x0));+        float ys = InterpHermite((float)(yf - y0));+        float zs = InterpHermite((float)(zf - z0));++        x0 *= PrimeX;+        y0 *= PrimeY;+        z0 *= PrimeZ;+        int x1 = x0 + PrimeX;+        int y1 = y0 + PrimeY;+        int z1 = z0 + PrimeZ;++        int hash0 = Hash(seed, x0, y0, z0) & (255 << 2);+        int hash1 = Hash(seed, x1, y0, z0) & (255 << 2);++        float lx0x = Lerp(Lookup<float>::RandVecs3D[hash0], Lookup<float>::RandVecs3D[hash1], xs);+        float ly0x = Lerp(Lookup<float>::RandVecs3D[hash0 | 1], Lookup<float>::RandVecs3D[hash1 | 1], xs);+        float lz0x = Lerp(Lookup<float>::RandVecs3D[hash0 | 2], Lookup<float>::RandVecs3D[hash1 | 2], xs);++        hash0 = Hash(seed, x0, y1, z0) & (255 << 2);+        hash1 = Hash(seed, x1, y1, z0) & (255 << 2);++        float lx1x = Lerp(Lookup<float>::RandVecs3D[hash0], Lookup<float>::RandVecs3D[hash1], xs);+        float ly1x = Lerp(Lookup<float>::RandVecs3D[hash0 | 1], Lookup<float>::RandVecs3D[hash1 | 1], xs);+        float lz1x = Lerp(Lookup<float>::RandVecs3D[hash0 | 2], Lookup<float>::RandVecs3D[hash1 | 2], xs);++        float lx0y = Lerp(lx0x, lx1x, ys);+        float ly0y = Lerp(ly0x, ly1x, ys);+        float lz0y = Lerp(lz0x, lz1x, ys);++        hash0 = Hash(seed, x0, y0, z1) & (255 << 2);+        hash1 = Hash(seed, x1, y0, z1) & (255 << 2);++        lx0x = Lerp(Lookup<float>::RandVecs3D[hash0], Lookup<float>::RandVecs3D[hash1], xs);+        ly0x = Lerp(Lookup<float>::RandVecs3D[hash0 | 1], Lookup<float>::RandVecs3D[hash1 | 1], xs);+        lz0x = Lerp(Lookup<float>::RandVecs3D[hash0 | 2], Lookup<float>::RandVecs3D[hash1 | 2], xs);++        hash0 = Hash(seed, x0, y1, z1) & (255 << 2);+        hash1 = Hash(seed, x1, y1, z1) & (255 << 2);++        lx1x = Lerp(Lookup<float>::RandVecs3D[hash0], Lookup<float>::RandVecs3D[hash1], xs);+        ly1x = Lerp(Lookup<float>::RandVecs3D[hash0 | 1], Lookup<float>::RandVecs3D[hash1 | 1], xs);+        lz1x = Lerp(Lookup<float>::RandVecs3D[hash0 | 2], Lookup<float>::RandVecs3D[hash1 | 2], xs);++        xr += Lerp(lx0y, Lerp(lx0x, lx1x, ys), zs) * warpAmp;+        yr += Lerp(ly0y, Lerp(ly0x, ly1x, ys), zs) * warpAmp;+        zr += Lerp(lz0y, Lerp(lz0x, lz1x, ys), zs) * warpAmp;+    }+++    // Domain Warp Simplex/OpenSimplex2++    template <typename FNfloat>+    void SingleDomainWarpSimplexGradient(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat& xr, FNfloat& yr, bool outGradOnly) const+    {+        const float SQRT3 = 1.7320508075688772935274463415059f;+        const float G2 = (3 - SQRT3) / 6;++        x *= frequency;+        y *= frequency;++        /*+         * --- Skew moved to TransformNoiseCoordinate method ---+         * const FNfloat F2 = 0.5f * (SQRT3 - 1);+         * FNfloat s = (x + y) * F2;+         * x += s; y += s;+        */++        int i = FastFloor(x);+        int j = FastFloor(y);+        float xi = (float)(x - i);+        float yi = (float)(y - j);++        float t = (xi + yi) * G2;+        float x0 = (float)(xi - t);+        float y0 = (float)(yi - t);++        i *= PrimeX;+        j *= PrimeY;++        float vx, vy;+        vx = vy = 0;++        float a = 0.5f - x0 * x0 - y0 * y0;+        if (a > 0)+        {+            float aaaa = (a * a) * (a * a);+            float xo, yo;+            if (outGradOnly)+                GradCoordOut(seed, i, j, xo, yo);+            else+                GradCoordDual(seed, i, j, x0, y0, xo, yo);+            vx += aaaa * xo;+            vy += aaaa * yo;+        }++        float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a);+        if (c > 0)+        {+            float x2 = x0 + (2 * (float)G2 - 1);+            float y2 = y0 + (2 * (float)G2 - 1);+            float cccc = (c * c) * (c * c);+            float xo, yo;+            if (outGradOnly)+                GradCoordOut(seed, i + PrimeX, j + PrimeY, xo, yo);+            else+                GradCoordDual(seed, i + PrimeX, j + PrimeY, x2, y2, xo, yo);+            vx += cccc * xo;+            vy += cccc * yo;+        }++        if (y0 > x0)+        {+            float x1 = x0 + (float)G2;+            float y1 = y0 + ((float)G2 - 1);+            float b = 0.5f - x1 * x1 - y1 * y1;+            if (b > 0)+            {+                float bbbb = (b * b) * (b * b);+                float xo, yo;+                if (outGradOnly)+                    GradCoordOut(seed, i, j + PrimeY, xo, yo);+                else+                    GradCoordDual(seed, i, j + PrimeY, x1, y1, xo, yo);+                vx += bbbb * xo;+                vy += bbbb * yo;+            }+        }+        else+        {+            float x1 = x0 + ((float)G2 - 1);+            float y1 = y0 + (float)G2;+            float b = 0.5f - x1 * x1 - y1 * y1;+            if (b > 0)+            {+                float bbbb = (b * b) * (b * b);+                float xo, yo;+                if (outGradOnly)+                    GradCoordOut(seed, i + PrimeX, j, xo, yo);+                else+                    GradCoordDual(seed, i + PrimeX, j, x1, y1, xo, yo);+                vx += bbbb * xo;+                vy += bbbb * yo;+            }+        }++        xr += vx * warpAmp;+        yr += vy * warpAmp;+    }++    template <typename FNfloat>+    void SingleDomainWarpOpenSimplex2Gradient(int seed, float warpAmp, float frequency, FNfloat x, FNfloat y, FNfloat z, FNfloat& xr, FNfloat& yr, FNfloat& zr, bool outGradOnly) const+    {+        x *= frequency;+        y *= frequency;+        z *= frequency;++        /*+         * --- Rotation moved to TransformDomainWarpCoordinate method ---+         * const FNfloat R3 = (FNfloat)(2.0 / 3.0);+         * FNfloat r = (x + y + z) * R3; // Rotation, not skew+         * x = r - x; y = r - y; z = r - z;+        */++        int i = FastRound(x);+        int j = FastRound(y);+        int k = FastRound(z);+        float x0 = (float)x - i;+        float y0 = (float)y - j;+        float z0 = (float)z - k;++        int xNSign = (int)(-x0 - 1.0f) | 1;+        int yNSign = (int)(-y0 - 1.0f) | 1;+        int zNSign = (int)(-z0 - 1.0f) | 1;++        float ax0 = xNSign * -x0;+        float ay0 = yNSign * -y0;+        float az0 = zNSign * -z0;++        i *= PrimeX;+        j *= PrimeY;+        k *= PrimeZ;++        float vx, vy, vz;+        vx = vy = vz = 0;++        float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0);+        for (int l = 0; l < 2; l++)+        {+            if (a > 0)+            {+                float aaaa = (a * a) * (a * a);+                float xo, yo, zo;+                if (outGradOnly)+                    GradCoordOut(seed, i, j, k, xo, yo, zo);+                else+                    GradCoordDual(seed, i, j, k, x0, y0, z0, xo, yo, zo);+                vx += aaaa * xo;+                vy += aaaa * yo;+                vz += aaaa * zo;+            }++            float b = a + 1;+            int i1 = i;+            int j1 = j;+            int k1 = k;+            float x1 = x0;+            float y1 = y0;+            float z1 = z0;++            if (ax0 >= ay0 && ax0 >= az0)+            {+                x1 += xNSign;+                b -= xNSign * 2 * x1;+                i1 -= xNSign * PrimeX;+            }+            else if (ay0 > ax0 && ay0 >= az0)+            {+                y1 += yNSign;+                b -= yNSign * 2 * y1;+                j1 -= yNSign * PrimeY;+            }+            else+            {+                z1 += zNSign;+                b -= zNSign * 2 * z1;+                k1 -= zNSign * PrimeZ;+            }++            if (b > 0)+            {+                float bbbb = (b * b) * (b * b);+                float xo, yo, zo;+                if (outGradOnly)+                    GradCoordOut(seed, i1, j1, k1, xo, yo, zo);+                else+                    GradCoordDual(seed, i1, j1, k1, x1, y1, z1, xo, yo, zo);+                vx += bbbb * xo;+                vy += bbbb * yo;+                vz += bbbb * zo;+            }++            if (l == 1) break;++            ax0 = 0.5f - ax0;+            ay0 = 0.5f - ay0;+            az0 = 0.5f - az0;++            x0 = xNSign * ax0;+            y0 = yNSign * ay0;+            z0 = zNSign * az0;++            a += (0.75f - ax0) - (ay0 + az0);++            i += (xNSign >> 1) & PrimeX;+            j += (yNSign >> 1) & PrimeY;+            k += (zNSign >> 1) & PrimeZ;++            xNSign = -xNSign;+            yNSign = -yNSign;+            zNSign = -zNSign;++            seed += 1293373;+        }++        xr += vx * warpAmp;+        yr += vy * warpAmp;+        zr += vz * warpAmp;+    }+};++template <>+struct FastNoiseLite::Arguments_must_be_floating_point_values<float> {};+template <>+struct FastNoiseLite::Arguments_must_be_floating_point_values<double> {};+template <>+struct FastNoiseLite::Arguments_must_be_floating_point_values<long double> {};++template <typename T>+const T FastNoiseLite::Lookup<T>::Gradients2D[] =+{+    0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,+    0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,+    0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,+    -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,+    -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,+    -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,+    0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,+    0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,+    0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,+    -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,+    -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,+    -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,+    0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,+    0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,+    0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,+    -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,+    -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,+    -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,+    0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,+    0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,+    0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,+    -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,+    -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,+    -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,+    0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,+    0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,+    0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,+    -0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,+    -0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,+    -0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,+    0.38268343236509f, 0.923879532511287f, 0.923879532511287f, 0.38268343236509f, 0.923879532511287f, -0.38268343236509f, 0.38268343236509f, -0.923879532511287f,+    -0.38268343236509f, -0.923879532511287f, -0.923879532511287f, -0.38268343236509f, -0.923879532511287f, 0.38268343236509f, -0.38268343236509f, 0.923879532511287f,+};++template <typename T>+const T FastNoiseLite::Lookup<T>::RandVecs2D[] =+{+    -0.2700222198f, -0.9628540911f, 0.3863092627f, -0.9223693152f, 0.04444859006f, -0.999011673f, -0.5992523158f, -0.8005602176f, -0.7819280288f, 0.6233687174f, 0.9464672271f, 0.3227999196f, -0.6514146797f, -0.7587218957f, 0.9378472289f, 0.347048376f,+    -0.8497875957f, -0.5271252623f, -0.879042592f, 0.4767432447f, -0.892300288f, -0.4514423508f, -0.379844434f, -0.9250503802f, -0.9951650832f, 0.0982163789f, 0.7724397808f, -0.6350880136f, 0.7573283322f, -0.6530343002f, -0.9928004525f, -0.119780055f,+    -0.0532665713f, 0.9985803285f, 0.9754253726f, -0.2203300762f, -0.7665018163f, 0.6422421394f, 0.991636706f, 0.1290606184f, -0.994696838f, 0.1028503788f, -0.5379205513f, -0.84299554f, 0.5022815471f, -0.8647041387f, 0.4559821461f, -0.8899889226f,+    -0.8659131224f, -0.5001944266f, 0.0879458407f, -0.9961252577f, -0.5051684983f, 0.8630207346f, 0.7753185226f, -0.6315704146f, -0.6921944612f, 0.7217110418f, -0.5191659449f, -0.8546734591f, 0.8978622882f, -0.4402764035f, -0.1706774107f, 0.9853269617f,+    -0.9353430106f, -0.3537420705f, -0.9992404798f, 0.03896746794f, -0.2882064021f, -0.9575683108f, -0.9663811329f, 0.2571137995f, -0.8759714238f, -0.4823630009f, -0.8303123018f, -0.5572983775f, 0.05110133755f, -0.9986934731f, -0.8558373281f, -0.5172450752f,+    0.09887025282f, 0.9951003332f, 0.9189016087f, 0.3944867976f, -0.2439375892f, -0.9697909324f, -0.8121409387f, -0.5834613061f, -0.9910431363f, 0.1335421355f, 0.8492423985f, -0.5280031709f, -0.9717838994f, -0.2358729591f, 0.9949457207f, 0.1004142068f,+    0.6241065508f, -0.7813392434f, 0.662910307f, 0.7486988212f, -0.7197418176f, 0.6942418282f, -0.8143370775f, -0.5803922158f, 0.104521054f, -0.9945226741f, -0.1065926113f, -0.9943027784f, 0.445799684f, -0.8951327509f, 0.105547406f, 0.9944142724f,+    -0.992790267f, 0.1198644477f, -0.8334366408f, 0.552615025f, 0.9115561563f, -0.4111755999f, 0.8285544909f, -0.5599084351f, 0.7217097654f, -0.6921957921f, 0.4940492677f, -0.8694339084f, -0.3652321272f, -0.9309164803f, -0.9696606758f, 0.2444548501f,+    0.08925509731f, -0.996008799f, 0.5354071276f, -0.8445941083f, -0.1053576186f, 0.9944343981f, -0.9890284586f, 0.1477251101f, 0.004856104961f, 0.9999882091f, 0.9885598478f, 0.1508291331f, 0.9286129562f, -0.3710498316f, -0.5832393863f, -0.8123003252f,+    0.3015207509f, 0.9534596146f, -0.9575110528f, 0.2883965738f, 0.9715802154f, -0.2367105511f, 0.229981792f, 0.9731949318f, 0.955763816f, -0.2941352207f, 0.740956116f, 0.6715534485f, -0.9971513787f, -0.07542630764f, 0.6905710663f, -0.7232645452f,+    -0.290713703f, -0.9568100872f, 0.5912777791f, -0.8064679708f, -0.9454592212f, -0.325740481f, 0.6664455681f, 0.74555369f, 0.6236134912f, 0.7817328275f, 0.9126993851f, -0.4086316587f, -0.8191762011f, 0.5735419353f, -0.8812745759f, -0.4726046147f,+    0.9953313627f, 0.09651672651f, 0.9855650846f, -0.1692969699f, -0.8495980887f, 0.5274306472f, 0.6174853946f, -0.7865823463f, 0.8508156371f, 0.52546432f, 0.9985032451f, -0.05469249926f, 0.1971371563f, -0.9803759185f, 0.6607855748f, -0.7505747292f,+    -0.03097494063f, 0.9995201614f, -0.6731660801f, 0.739491331f, -0.7195018362f, -0.6944905383f, 0.9727511689f, 0.2318515979f, 0.9997059088f, -0.0242506907f, 0.4421787429f, -0.8969269532f, 0.9981350961f, -0.061043673f, -0.9173660799f, -0.3980445648f,+    -0.8150056635f, -0.5794529907f, -0.8789331304f, 0.4769450202f, 0.0158605829f, 0.999874213f, -0.8095464474f, 0.5870558317f, -0.9165898907f, -0.3998286786f, -0.8023542565f, 0.5968480938f, -0.5176737917f, 0.8555780767f, -0.8154407307f, -0.5788405779f,+    0.4022010347f, -0.9155513791f, -0.9052556868f, -0.4248672045f, 0.7317445619f, 0.6815789728f, -0.5647632201f, -0.8252529947f, -0.8403276335f, -0.5420788397f, -0.9314281527f, 0.363925262f, 0.5238198472f, 0.8518290719f, 0.7432803869f, -0.6689800195f,+    -0.985371561f, -0.1704197369f, 0.4601468731f, 0.88784281f, 0.825855404f, 0.5638819483f, 0.6182366099f, 0.7859920446f, 0.8331502863f, -0.553046653f, 0.1500307506f, 0.9886813308f, -0.662330369f, -0.7492119075f, -0.668598664f, 0.743623444f,+    0.7025606278f, 0.7116238924f, -0.5419389763f, -0.8404178401f, -0.3388616456f, 0.9408362159f, 0.8331530315f, 0.5530425174f, -0.2989720662f, -0.9542618632f, 0.2638522993f, 0.9645630949f, 0.124108739f, -0.9922686234f, -0.7282649308f, -0.6852956957f,+    0.6962500149f, 0.7177993569f, -0.9183535368f, 0.3957610156f, -0.6326102274f, -0.7744703352f, -0.9331891859f, -0.359385508f, -0.1153779357f, -0.9933216659f, 0.9514974788f, -0.3076565421f, -0.08987977445f, -0.9959526224f, 0.6678496916f, 0.7442961705f,+    0.7952400393f, -0.6062947138f, -0.6462007402f, -0.7631674805f, -0.2733598753f, 0.9619118351f, 0.9669590226f, -0.254931851f, -0.9792894595f, 0.2024651934f, -0.5369502995f, -0.8436138784f, -0.270036471f, -0.9628500944f, -0.6400277131f, 0.7683518247f,+    -0.7854537493f, -0.6189203566f, 0.06005905383f, -0.9981948257f, -0.02455770378f, 0.9996984141f, -0.65983623f, 0.751409442f, -0.6253894466f, -0.7803127835f, -0.6210408851f, -0.7837781695f, 0.8348888491f, 0.5504185768f, -0.1592275245f, 0.9872419133f,+    0.8367622488f, 0.5475663786f, -0.8675753916f, -0.4973056806f, -0.2022662628f, -0.9793305667f, 0.9399189937f, 0.3413975472f, 0.9877404807f, -0.1561049093f, -0.9034455656f, 0.4287028224f, 0.1269804218f, -0.9919052235f, -0.3819600854f, 0.924178821f,+    0.9754625894f, 0.2201652486f, -0.3204015856f, -0.9472818081f, -0.9874760884f, 0.1577687387f, 0.02535348474f, -0.9996785487f, 0.4835130794f, -0.8753371362f, -0.2850799925f, -0.9585037287f, -0.06805516006f, -0.99768156f, -0.7885244045f, -0.6150034663f,+    0.3185392127f, -0.9479096845f, 0.8880043089f, 0.4598351306f, 0.6476921488f, -0.7619021462f, 0.9820241299f, 0.1887554194f, 0.9357275128f, -0.3527237187f, -0.8894895414f, 0.4569555293f, 0.7922791302f, 0.6101588153f, 0.7483818261f, 0.6632681526f,+    -0.7288929755f, -0.6846276581f, 0.8729032783f, -0.4878932944f, 0.8288345784f, 0.5594937369f, 0.08074567077f, 0.9967347374f, 0.9799148216f, -0.1994165048f, -0.580730673f, -0.8140957471f, -0.4700049791f, -0.8826637636f, 0.2409492979f, 0.9705377045f,+    0.9437816757f, -0.3305694308f, -0.8927998638f, -0.4504535528f, -0.8069622304f, 0.5906030467f, 0.06258973166f, 0.9980393407f, -0.9312597469f, 0.3643559849f, 0.5777449785f, 0.8162173362f, -0.3360095855f, -0.941858566f, 0.697932075f, -0.7161639607f,+    -0.002008157227f, -0.9999979837f, -0.1827294312f, -0.9831632392f, -0.6523911722f, 0.7578824173f, -0.4302626911f, -0.9027037258f, -0.9985126289f, -0.05452091251f, -0.01028102172f, -0.9999471489f, -0.4946071129f, 0.8691166802f, -0.2999350194f, 0.9539596344f,+    0.8165471961f, 0.5772786819f, 0.2697460475f, 0.962931498f, -0.7306287391f, -0.6827749597f, -0.7590952064f, -0.6509796216f, -0.907053853f, 0.4210146171f, -0.5104861064f, -0.8598860013f, 0.8613350597f, 0.5080373165f, 0.5007881595f, -0.8655698812f,+    -0.654158152f, 0.7563577938f, -0.8382755311f, -0.545246856f, 0.6940070834f, 0.7199681717f, 0.06950936031f, 0.9975812994f, 0.1702942185f, -0.9853932612f, 0.2695973274f, 0.9629731466f, 0.5519612192f, -0.8338697815f, 0.225657487f, -0.9742067022f,+    0.4215262855f, -0.9068161835f, 0.4881873305f, -0.8727388672f, -0.3683854996f, -0.9296731273f, -0.9825390578f, 0.1860564427f, 0.81256471f, 0.5828709909f, 0.3196460933f, -0.9475370046f, 0.9570913859f, 0.2897862643f, -0.6876655497f, -0.7260276109f,+    -0.9988770922f, -0.047376731f, -0.1250179027f, 0.992154486f, -0.8280133617f, 0.560708367f, 0.9324863769f, -0.3612051451f, 0.6394653183f, 0.7688199442f, -0.01623847064f, -0.9998681473f, -0.9955014666f, -0.09474613458f, -0.81453315f, 0.580117012f,+    0.4037327978f, -0.9148769469f, 0.9944263371f, 0.1054336766f, -0.1624711654f, 0.9867132919f, -0.9949487814f, -0.100383875f, -0.6995302564f, 0.7146029809f, 0.5263414922f, -0.85027327f, -0.5395221479f, 0.841971408f, 0.6579370318f, 0.7530729462f,+    0.01426758847f, -0.9998982128f, -0.6734383991f, 0.7392433447f, 0.639412098f, -0.7688642071f, 0.9211571421f, 0.3891908523f, -0.146637214f, -0.9891903394f, -0.782318098f, 0.6228791163f, -0.5039610839f, -0.8637263605f, -0.7743120191f, -0.6328039957f,+};++template <typename T>+const T FastNoiseLite::Lookup<T>::Gradients3D[] =+{+    0, 1, 1, 0,  0,-1, 1, 0,  0, 1,-1, 0,  0,-1,-1, 0,+    1, 0, 1, 0, -1, 0, 1, 0,  1, 0,-1, 0, -1, 0,-1, 0,+    1, 1, 0, 0, -1, 1, 0, 0,  1,-1, 0, 0, -1,-1, 0, 0,+    0, 1, 1, 0,  0,-1, 1, 0,  0, 1,-1, 0,  0,-1,-1, 0,+    1, 0, 1, 0, -1, 0, 1, 0,  1, 0,-1, 0, -1, 0,-1, 0,+    1, 1, 0, 0, -1, 1, 0, 0,  1,-1, 0, 0, -1,-1, 0, 0,+    0, 1, 1, 0,  0,-1, 1, 0,  0, 1,-1, 0,  0,-1,-1, 0,+    1, 0, 1, 0, -1, 0, 1, 0,  1, 0,-1, 0, -1, 0,-1, 0,+    1, 1, 0, 0, -1, 1, 0, 0,  1,-1, 0, 0, -1,-1, 0, 0,+    0, 1, 1, 0,  0,-1, 1, 0,  0, 1,-1, 0,  0,-1,-1, 0,+    1, 0, 1, 0, -1, 0, 1, 0,  1, 0,-1, 0, -1, 0,-1, 0,+    1, 1, 0, 0, -1, 1, 0, 0,  1,-1, 0, 0, -1,-1, 0, 0,+    0, 1, 1, 0,  0,-1, 1, 0,  0, 1,-1, 0,  0,-1,-1, 0,+    1, 0, 1, 0, -1, 0, 1, 0,  1, 0,-1, 0, -1, 0,-1, 0,+    1, 1, 0, 0, -1, 1, 0, 0,  1,-1, 0, 0, -1,-1, 0, 0,+    1, 1, 0, 0,  0,-1, 1, 0, -1, 1, 0, 0,  0,-1,-1, 0+};++template <typename T>+const T FastNoiseLite::Lookup<T>::RandVecs3D[] =+{+    -0.7292736885f, -0.6618439697f, 0.1735581948f, 0, 0.790292081f, -0.5480887466f, -0.2739291014f, 0, 0.7217578935f, 0.6226212466f, 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0.5975094525f, 0, -0.3595449969f, -0.8885529948f, 0.28495784f, 0, -0.2180405296f, 0.1529888965f, 0.9638738118f, 0, -0.7277432317f, -0.6164050508f, -0.3007234646f, 0, 0.7249729114f, -0.00669719484f, 0.6887448187f, 0, -0.5553659455f, -0.5336586252f, 0.6377908264f, 0, 0.5137558015f, 0.7976208196f, -0.3160000073f, 0,+    -0.3794024848f, 0.9245608561f, -0.03522751494f, 0, 0.8229248658f, 0.2745365933f, -0.4974176556f, 0, -0.5404114394f, 0.6091141441f, 0.5804613989f, 0, 0.8036581901f, -0.2703029469f, 0.5301601931f, 0, 0.6044318879f, 0.6832968393f, 0.4095943388f, 0, 0.06389988817f, 0.9658208605f, -0.2512108074f, 0, 0.1087113286f, 0.7402471173f, -0.6634877936f, 0, -0.713427712f, -0.6926784018f, 0.1059128479f, 0,+    0.6458897819f, -0.5724548511f, -0.5050958653f, 0, -0.6553931414f, 0.7381471625f, 0.159995615f, 0, 0.3910961323f, 0.9188871375f, -0.05186755998f, 0, -0.4879022471f, -0.5904376907f, 0.6429111375f, 0, 0.6014790094f, 0.7707441366f, -0.2101820095f, 0, -0.5677173047f, 0.7511360995f, 0.3368851762f, 0, 0.7858573506f, 0.226674665f, 0.5753666838f, 0, -0.4520345543f, -0.604222686f, -0.6561857263f, 0,+    0.002272116345f, 0.4132844051f, -0.9105991643f, 0, -0.5815751419f, -0.5162925989f, 0.6286591339f, 0, -0.03703704785f, 0.8273785755f, 0.5604221175f, 0, -0.5119692504f, 0.7953543429f, -0.3244980058f, 0, -0.2682417366f, -0.9572290247f, -0.1084387619f, 0, -0.2322482736f, -0.9679131102f, -0.09594243324f, 0, 0.3554328906f, -0.8881505545f, 0.2913006227f, 0, 0.7346520519f, -0.4371373164f, 0.5188422971f, 0,+    0.9985120116f, 0.04659011161f, -0.02833944577f, 0, -0.3727687496f, -0.9082481361f, 0.1900757285f, 0, 0.91737377f, -0.3483642108f, 0.1925298489f, 0, 0.2714911074f, 0.4147529736f, -0.8684886582f, 0, 0.5131763485f, -0.7116334161f, 0.4798207128f, 0, -0.8737353606f, 0.18886992f, -0.4482350644f, 0, 0.8460043821f, -0.3725217914f, 0.3814499973f, 0, 0.8978727456f, -0.1780209141f, -0.4026575304f, 0,+    0.2178065647f, -0.9698322841f, -0.1094789531f, 0, -0.1518031304f, -0.7788918132f, -0.6085091231f, 0, -0.2600384876f, -0.4755398075f, -0.8403819825f, 0, 0.572313509f, -0.7474340931f, -0.3373418503f, 0, -0.7174141009f, 0.1699017182f, -0.6756111411f, 0, -0.684180784f, 0.02145707593f, -0.7289967412f, 0, -0.2007447902f, 0.06555605789f, -0.9774476623f, 0, -0.1148803697f, -0.8044887315f, 0.5827524187f, 0,+    -0.7870349638f, 0.03447489231f, 0.6159443543f, 0, -0.2015596421f, 0.6859872284f, 0.6991389226f, 0, -0.08581082512f, -0.10920836f, -0.9903080513f, 0, 0.5532693395f, 0.7325250401f, -0.396610771f, 0, -0.1842489331f, -0.9777375055f, -0.1004076743f, 0, 0.0775473789f, -0.9111505856f, 0.4047110257f, 0, 0.1399838409f, 0.7601631212f, -0.6344734459f, 0, 0.4484419361f, -0.845289248f, 0.2904925424f, 0+};++#endif
+ bench/fnl-compare/fnl_bench_shim.cpp view
@@ -0,0 +1,54 @@+// Bulk-loop shim over the vendored FastNoiseLite.h (./cbits/FastNoiseLite.h)+// to provide a fair comparison to FNL.+//+// Sticking the loop in C++ should prevent FFI overhead from skewing results. +// Unsafe calls should have double-digit nanosecond overhead, so the signal from +// the bench itself should dominate.+//+// tasty-bench handles timing and statistics; simpler and less numerically fraught +// than trying to cross-compare Google benchmark to tasty/criterion.+//+// This should be compiled the way a user would build FNL: -O3 -march=native. We+// want to give C++ every edge it can have for a meaningful comparison.+//+// NOTE: noiseType convention is:+//   0=OpenSimplex2 +//   1=OpenSimplex2S +//   2=Cellular +//   3=Perlin +//   4=ValueCubic +//   5=Value+#include "FastNoiseLite.h"++static FastNoiseLite mk(int noiseType, int seed, float freq) {+    FastNoiseLite fnl(seed);+    fnl.SetNoiseType(static_cast<FastNoiseLite::NoiseType>(noiseType));+    // pure-noise's loop multiplies every coordinate by a runtime k; FNL pays+    // the same multiply here via mFrequency.+    fnl.SetFrequency(freq);+    if (noiseType == 2) { // match audit-bench: Euclidean distance, Distance result+        fnl.SetCellularDistanceFunction(FastNoiseLite::CellularDistanceFunction_Euclidean);+        fnl.SetCellularReturnType(FastNoiseLite::CellularReturnType_Distance);+    }+    return fnl;+}++extern "C" {++float fnl_bench_sum2(int noiseType, int seed, float freq, int n,+                     const float* __restrict xs, const float* __restrict ys) {+    FastNoiseLite fnl = mk(noiseType, seed, freq);+    float acc = 0.0f;+    for (int i = 0; i < n; i++) acc += fnl.GetNoise(xs[i], ys[i]);+    return acc;+}++float fnl_bench_sum3(int noiseType, int seed, float freq, int n,+                     const float* __restrict xs, const float* __restrict ys, const float* __restrict zs) {+    FastNoiseLite fnl = mk(noiseType, seed, freq);+    float acc = 0.0f;+    for (int i = 0; i < n; i++) acc += fnl.GetNoise(xs[i], ys[i], zs[i]);+    return acc;+}++} // extern "C"
pure-noise.cabal view
@@ -1,43 +1,85 @@ cabal-version: 2.2 --- This file has been generated from package.yaml by hpack version 0.37.0.+-- This file has been generated from package.yaml by hpack version 0.39.6. -- -- see: https://github.com/sol/hpack  name:           pure-noise-version:        0.1.0.1-synopsis:       Performant, modern noise generation for Haskell with minimal dependencies. Based on FastNoiseLite.-description:    Please see the README on GitHub at <https://github.com/jtnuttall/pure-noise#readme>+version:        0.2.2.0+synopsis:       Performant, modern noise generation (Perlin, OpenSimplex2, Cellular)+description:    Fast, modern noise generation In pure Haskell with an algebraic interface.+                Provides Perlin, OpenSimplex2, OpenSimplex2S, Value, and Cellular noise variants. category:       Math, Numeric, Noise homepage:       https://github.com/jtnuttall/pure-noise#readme bug-reports:    https://github.com/jtnuttall/pure-noise/issues author:         Jeremy Nuttall maintainer:     jeremy@jeremy-nuttall.com-copyright:      2024 Jeremy Nuttall+copyright:      2026 Jeremy Nuttall license:        BSD-3-Clause license-file:   LICENSE build-type:     Simple+tested-with:+    GHC == 9.6.7+  , GHC == 9.8.4+  , GHC == 9.12.2 extra-source-files:     README.md+    LICENSE+    LICENSE_FastNoiseLite+    bench/fnl-compare/cbits/FastNoiseLite.h+extra-doc-files:     CHANGELOG.md  source-repository head   type: git   location: https://github.com/jtnuttall/pure-noise +flag llvm-bench+  description: Build the benchmark suites via GHC's LLVM backend with a pinned toolchain+               (-fllvm, -pgmlo opt, -pgmlc llc, -pgmlas clang) plus -mavx -mfma and fast+               FP contraction in llc (-optlc-fp-contract=fast). Requires opt/llc/clang+               on PATH (LLVM <= 19 for GHC 9.12) and GHC >= 9.10 (for -pgmlas). Off by+               default so `cabal build --enable-benchmarks` works on machines and CI+               runners without LLVM. Published benchmark numbers are collected with this+               flag on; see bench/README.md.+  manual: True+  default: False++flag mavx+  description: Compile with AVX instructions+  manual: True+  default: False++flag mfma+  description: Compile with native fused-multiply-add instructions+  manual: True+  default: False++flag optimize+  description: Turns on -O2 for pure-noise. Since the library is pretty small, this shouldn't be+               too much trouble, but you can disable this flag if it's slowing your builds too+               much.+               .+               Rationale:+               - -O1 leaves ~3x on the table for tight noise loops in downstream code.+               - -O2 seems to produce higher-quality unfoldings, which in turn causes pure-noise's+               kernels to inline and optimize more reliably at call sites.+  manual: True+  default: True+ library   exposed-modules:       Numeric.Noise       Numeric.Noise.Cellular       Numeric.Noise.Fractal-      Numeric.Noise.Internal-      Numeric.Noise.Internal.Math       Numeric.Noise.OpenSimplex       Numeric.Noise.Perlin       Numeric.Noise.SuperSimplex       Numeric.Noise.Value       Numeric.Noise.ValueCubic   other-modules:+      Numeric.Noise.Internal+      Numeric.Noise.Internal.Math       Paths_pure_noise   autogen-modules:       Paths_pure_noise@@ -45,31 +87,58 @@       src   ghc-options: -Wall -Wcompat -Widentities -Wincomplete-record-updates -Wincomplete-uni-patterns -Wmissing-export-lists -Wmissing-home-modules -Wpartial-fields -Wredundant-constraints   build-depends:-      base >=4.7 && <5-    , vector <=0.14+      base >=4.16 && <5+    , primitive >=0.8 && <0.10   default-language: GHC2021+  if flag(optimize)+    ghc-options: -O2+  if flag(mfma)+    ghc-options: -mfma+    cpp-options: -DHAS_FMA+  if flag(mavx)+    ghc-options: -mavx+    cpp-options: -DHAS_AVX  test-suite pure-noise-test   type: exitcode-stdio-1.0   main-is: Driver.hs   other-modules:+      CellularSpec+      FractalSpec+      Golden.Util       Noise2Spec       Noise3Spec+      OpenSimplexSpec       PerlinSpec+      SuperSimplexSpec+      TotalitySpec+      ValueCubicSpec+      ValueSpec       Paths_pure_noise   autogen-modules:       Paths_pure_noise   hs-source-dirs:       test   ghc-options: -Wall -Wcompat -Widentities -Wincomplete-record-updates -Wincomplete-uni-patterns -Wmissing-export-lists -Wmissing-home-modules -Wpartial-fields -Wredundant-constraints -Wno-missing-export-lists -threaded -rtsopts -with-rtsopts=-N+  build-tool-depends:+      tasty-discover:tasty-discover   build-depends:-      base >=4.7 && <5+      JuicyPixels ==3.3.*+    , aeson >=2.0 && <2.3+    , aeson-pretty+    , base >=4.16 && <5+    , bytestring+    , directory+    , filepath+    , massiv >=1.0 && <2.0+    , primitive >=0.8 && <0.10     , pure-noise     , tasty-    , tasty-discover+    , tasty-golden     , tasty-hunit     , tasty-quickcheck-    , vector <=0.14+    , text+    , typed-process   default-language: GHC2021  benchmark pure-noise-bench@@ -82,13 +151,53 @@       Paths_pure_noise   hs-source-dirs:       bench-  ghc-options: -Wall -Wcompat -Widentities -Wincomplete-record-updates -Wincomplete-uni-patterns -Wmissing-export-lists -Wmissing-home-modules -Wpartial-fields -Wredundant-constraints -threaded -rtsopts -with-rtsopts=-N +RTS -A32m --nonmoving-gc -T -RTS -O2 -optc-O3 -fproc-alignment=64 -fsimpl-tick-factor=1000+  ghc-options: -Wall -Wcompat -Widentities -Wincomplete-record-updates -Wincomplete-uni-patterns -Wmissing-export-lists -Wmissing-home-modules -Wpartial-fields -Wredundant-constraints -threaded -rtsopts "-with-rtsopts=-N -A32m -T" -O2 -fsimpl-tick-factor=1000   build-depends:-      base >=4.7 && <5+      base >=4.16 && <5     , deepseq-    , mwc-random+    , massiv >=1.0 && <2.0+    , primitive >=0.8 && <0.10     , pure-noise+    , random     , tasty     , tasty-bench-    , vector <=0.14+    , vector >=0.12 && <0.14   default-language: GHC2021+  if flag(llvm-bench)+    ghc-options: -fllvm -pgmlo opt -pgmlc llc -pgmlas clang -mavx -mfma -optlc-fp-contract=fast++benchmark pure-noise-fnl-bench+  type: exitcode-stdio-1.0+  main-is: FnlBench.hs+  other-modules:+      Paths_pure_noise+  autogen-modules:+      Paths_pure_noise+  hs-source-dirs:+      bench/fnl-compare+  ghc-options: -Wall -Wcompat -Widentities -Wincomplete-record-updates -Wincomplete-uni-patterns -Wmissing-export-lists -Wmissing-home-modules -Wpartial-fields -Wredundant-constraints -threaded -rtsopts "-with-rtsopts=-A64m -T" -O2 -fsimpl-tick-factor=1000+  cxx-options: -O3 -std=c++14 -ffp-contract=fast -fstrict-overflow+  include-dirs:+      bench/fnl-compare/cbits+  cxx-sources:+      bench/fnl-compare/fnl_bench_shim.cpp+  build-depends:+      base >=4.16 && <5+    , mtl >=2.1 && <2.4+    , primitive >=0.8 && <0.10+    , pure-noise+    , splitmix ==0.1.*+    , tasty+    , tasty-bench >=0.4 && <0.6+    , vector >=0.12 && <0.14+  default-language: GHC2021+  if flag(llvm-bench)+    ghc-options: -fllvm -pgmlo opt -pgmlc llc -pgmlas clang -mavx -mfma -optlc-fp-contract=fast+  if arch(x86_64)+    cxx-options: -march=x86-64-v3+  if os(darwin)+    extra-libraries:+        c+++  else+    extra-libraries:+        stdc++
src/Numeric/Noise.hs view
@@ -1,112 +1,288 @@+{-# LANGUAGE DataKinds #-} {-# LANGUAGE Strict #-}  -- | -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com> -- Stability : experimental+--+-- Performant noise generation with composable noise functions.+--+-- Noise functions are built on a unified 'Noise' type that abstracts over+-- the seed and coordinate parameters. 'Noise2' and 'Noise3' are convenient+-- type aliases for 2D and 3D noise. These can be composed algebraically+-- with minimal performance overhead.+--+-- Noise values are generally clamped to @[-1, 1]@, although some noise+-- functions may occasionally produce values slightly outside this range.+--+-- == Basic Usage+--+-- Generate 2D Perlin noise:+--+-- @+-- import Numeric.Noise qualified as Noise+--+-- myNoise :: Noise.Seed -> Float -> Float -> Float+-- myNoise = Noise.noise2At Noise.perlin2+-- @+--+-- Compose multiple noise functions:+--+-- @+-- combined :: (RealFrac a) => Noise.Noise2 a+-- combined = (Noise.perlin2 + Noise.superSimplex2) / 2+--+-- myNoise2 :: Noise.Seed -> Float -> Float -> Float+-- myNoise2 = Noise.noise2At combined+-- @+--+-- Apply fractal Brownian motion:+--+-- @+-- fbm :: (RealFrac a) => Noise.Noise2 a+-- fbm = Noise.fractal2 Noise.defaultFractalConfig Noise.perlin2+-- @+--+-- == Advanced Features+--+-- Generate 1D noise by slicing higher-dimensional noise:+--+-- @+-- noise1d :: Noise.Noise1 Float+-- noise1d = Noise.sliceY2 0.5 Noise.perlin2+--+-- evaluate :: Float -> Float+-- evaluate = Noise.noise1At noise1d 0+-- @+--+-- Transform coordinates with 'warp':+--+-- @+-- scaledAndLayered :: Noise.Noise2 Float+-- scaledAndLayered =+--  Noise.warp (\\(x, y) -> (x * 2, y * 2)) Noise.perlin2+--    + fmap (* 0.5) Noise.perlin2+-- @+--+-- Layer independent noise with 'reseed' or 'next2':+--+-- @+-- layered :: Noise.Noise2 Float+-- layered = (Noise.perlin2 + Noise.next2 Noise.perlin2) \/ 2+-- @+--+-- == Coordinate domain+--+-- Coordinates are supported on the Int32 lattice range (@|x| < 2^31@; in+-- practice 'Float' precision runs out well before that).+--+-- The OpenSimplex2\/2S family first rotates coordinates into its lattice domain,+-- which shrinks its usable range by the rotation factor — up to ~1.73x, so roughly+-- @|x| < 1.2e9@.+--+-- Outside those domains, or for non-finite inputs, results are unspecified.+--+-- This behavior mirrors FastNoiseLite, but may change in a future major version. module Numeric.Noise (-  -- * Noise functions+  -- * Noise -  -- ** Noise functions-  module NoiseTypes,+  --++  -- | 'Noise1', 'Noise2', and 'Noise3' are type aliases for 1D, 2D, and 3D noise+  -- functions built on the unified 'Noise' type. They can be evaluated with+  -- 'noise1At', 'noise2At', and 'noise3At' respectively.+  --+  -- 'Seed' is a 'Data.Word.Word64' value used for deterministic noise generation.+  Noise,+  Noise1,+  Noise1',+  Noise2,+  Noise2',+  Noise3,+  Noise3',+  Seed,++  -- * Accessors+  noise1At,   noise2At,   noise3At, -  -- ** 2D Noise-  cellular2,+  -- * Noise functions++  -- ** Perlin+  perlin2,+  perlin3,++  -- ** OpenSimplex   openSimplex2,+  openSimplex3,++  -- ** OpenSimplex2S   superSimplex2,-  perlin2,+  superSimplex3,++  -- ** Cellular+  cellular2,+  cellular3,++  -- *** Configuration+  CellularConfig (..),+  defaultCellularConfig,+  CellularDistanceFn (..),+  CellularResult (..),++  -- ** Value   value2,   valueCubic2,--  -- ** 3D Noise-  perlin3,   value3,   valueCubic3, -  -- * Noise manipulation+  -- ** Constant fields+  const2,+  const3, -  -- ** Math utility functions-  module NoiseUtility,+  -- * Noise alteration -  -- ** Fractal Brownian Motion-  module Fractal,+  -- ** Altering values+  remap, -  -- ** Cellular noise configuration-  module Cellular,-) where+  -- ** Altering parameters+  warp,+  reseed,+  next2,+  next3, -import Numeric.Noise.Cellular as Cellular (-  CellularConfig (..),-  CellularDistanceFn (..),-  CellularResult (..),-  defaultCellularConfig,- )-import Numeric.Noise.Cellular qualified as Cellular-import Numeric.Noise.Fractal as Fractal-import Numeric.Noise.Internal-import Numeric.Noise.Internal as NoiseTypes (-  Noise2,-  Noise3,-  Seed,- )-import Numeric.Noise.Internal as NoiseUtility (+  -- ** Slicing (projecting)+  sliceX2,+  sliceX3,+  sliceY2,+  sliceY3,+  sliceZ3,++  -- * Fractals++  --++  -- | Fractal noise combines multiple octaves at different frequencies and+  -- amplitudes to create natural-looking, multi-scale patterns.+  --+  -- For custom fractal implementations using per-octave modifier functions,+  -- see "Numeric.Noise.Fractal".++  -- ** Fractal Brownian Motion (FBM)+  fractal2,+  fractal3,++  -- ** Fractal variants+  billow2,+  billow3,+  ridged2,+  ridged3,+  pingPong2,+  pingPong3,++  -- ** Configuration+  FractalConfig (..),+  defaultFractalConfig,+  PingPongStrength (..),+  defaultPingPongStrength,++  -- * Custom kernels++  --++  -- | Lift a plain @seed -> coordinates -> value@ function into a composable+  -- 'Noise' value — the inverses of the accessors above.+  --+  -- You may use these to construct custom kernels.+  mkNoise1,+  mkNoise2,+  mkNoise3,++  -- * Math utilities   clamp,   clamp2,   clamp3,   cubicInterp,   hermiteInterp,   lerp,-  next2,-  next3,   quinticInterp,- )+) where++import Numeric.Noise.Cellular (CellularConfig, CellularDistanceFn (..), CellularResult (..), defaultCellularConfig)+import Numeric.Noise.Cellular qualified as Cellular+import Numeric.Noise.Fractal+import Numeric.Noise.Internal import Numeric.Noise.OpenSimplex qualified as OpenSimplex import Numeric.Noise.Perlin qualified as Perlin import Numeric.Noise.SuperSimplex qualified as SuperSimplex import Numeric.Noise.Value qualified as Value import Numeric.Noise.ValueCubic qualified as ValueCubic -noise2At :: Noise2 a -> Seed -> a -> a -> a-noise2At = unNoise2-{-# INLINE noise2At #-}-+-- | 2D Cellular (Worley) noise. Configure with 'CellularConfig' to control+-- distance functions and return values.+--+-- Cellular noise creates patterns based on distances to randomly distributed+-- cell points. cellular2 :: (RealFrac a, Floating a) => CellularConfig a -> Noise2 a cellular2 = Cellular.noise2 {-# INLINE cellular2 #-} +-- | 3D Cellular (Worley) noise. See 'cellular2'.+cellular3 :: (RealFrac a, Floating a) => CellularConfig a -> Noise3 a+cellular3 = Cellular.noise3+{-# INLINE cellular3 #-}++-- | 2D OpenSimplex noise. Smooth gradient noise similar to Perlin but without+-- directional artifacts. openSimplex2 :: (RealFrac a) => Noise2 a openSimplex2 = OpenSimplex.noise2 {-# INLINE openSimplex2 #-} +-- | 3D OpenSimplex noise (FastNoiseLite's OpenSimplex2, two offset rotated+-- cube grids), including its default coordinate rotation.+openSimplex3 :: (RealFrac a) => Noise3 a+openSimplex3 = OpenSimplex.noise3+{-# INLINE openSimplex3 #-}++-- | 2D SuperSimplex noise. Improved OpenSimplex variant with better visual+-- characteristics. superSimplex2 :: (RealFrac a) => Noise2 a superSimplex2 = SuperSimplex.noise2 {-# INLINE superSimplex2 #-} +-- | 3D SuperSimplex noise (FastNoiseLite's OpenSimplex2S, two offset rotated+-- cube grids), including its default coordinate rotation.+superSimplex3 :: (RealFrac a) => Noise3 a+superSimplex3 = SuperSimplex.noise3+{-# INLINE superSimplex3 #-}++-- | 2D Perlin noise. Classic gradient noise algorithm. perlin2 :: (RealFrac a) => Noise2 a perlin2 = Perlin.noise2 {-# INLINE perlin2 #-} -noise3At :: Noise3 a -> Seed -> a -> a -> a -> a-noise3At = unNoise3-{-# INLINE noise3At #-}-+-- | 3D Perlin noise. Classic gradient noise algorithm. perlin3 :: (RealFrac a) => Noise3 a perlin3 = Perlin.noise3 {-# INLINE perlin3 #-} +-- | 2D Value noise. Simple noise based on interpolated random values at grid points. value2 :: (RealFrac a) => Noise2 a value2 = Value.noise2 {-# INLINE value2 #-} +-- | 3D Value noise. Simple noise based on interpolated random values at grid points. value3 :: (RealFrac a) => Noise3 a value3 = Value.noise3 {-# INLINE value3 #-} +-- | 2D Value noise with cubic interpolation for smoother results. valueCubic2 :: (RealFrac a) => Noise2 a valueCubic2 = ValueCubic.noise2 {-# INLINE valueCubic2 #-} +-- | 3D Value noise with cubic interpolation for smoother results. valueCubic3 :: (RealFrac a) => Noise3 a valueCubic3 = ValueCubic.noise3 {-# INLINE valueCubic3 #-}
src/Numeric/Noise/Cellular.hs view
@@ -1,6 +1,7 @@ {-# LANGUAGE LambdaCase #-} {-# LANGUAGE OverloadedLists #-} {-# LANGUAGE RecordWildCards #-}+{-# LANGUAGE StrictData #-}  -- | -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com>@@ -14,23 +15,35 @@    -- * 2D Noise   noise2,-  noise2BaseWith,++  -- * 3D Noise+  noise3, ) where  import Data.Bits-import Data.Foldable-import Data.Vector.Unboxed qualified as U+import Data.Foldable (foldl') -- redundant since GHC 9.10.1, here for compat+import Data.Primitive.PrimArray import GHC.Generics (Generic) import Numeric.Noise.Internal import Numeric.Noise.Internal.Math +-- | Configuration for cellular (Worley) noise generation.+--+-- Cellular noise is based on distances to randomly distributed cell points,+-- creating a distinctive cellular or organic pattern. data CellularConfig a = CellularConfig-  { cellularDistanceFn :: !CellularDistanceFn-  , cellularJitter :: !a-  , cellularResult :: !CellularResult+  { cellularDistanceFn :: CellularDistanceFn+  -- ^ Distance metric to use when computing distance to cell points.+  , cellularJitter :: a+  -- ^ Amount of randomness in cell point positions.+  -- \( 0 \) creates a regular grid, \( 1 \) creates fully random positions.+  -- Values outside \( [0, 1] \) may produce unusual results.+  , cellularResult :: CellularResult+  -- ^ What value to return from the noise function.   }   deriving (Generic, Show) +-- | Default configuration for cellular noise generation. defaultCellularConfig :: (RealFrac a) => CellularConfig a defaultCellularConfig =   CellularConfig@@ -38,22 +51,52 @@     , cellularJitter = 1     , cellularResult = CellValue     }+{-# INLINEABLE defaultCellularConfig #-} +-- | Distance function for cellular noise calculations.+--+-- Different distance metrics produce different visual characteristics+-- in the cellular pattern. data CellularDistanceFn-  = DistEuclidean-  | DistEuclideanSq-  | DistManhattan-  | DistHybrid+  = -- | \( \sqrt{dx^2 + dy^2} \) - Creates circular cells with smooth edges.+    DistEuclidean+  | -- | \( dx^2 + dy^2 \) - Faster than 'DistEuclidean' with similar appearance.+    DistEuclideanSq+  | -- | \( |dx| + |dy| \) - Creates diamond-shaped cells with sharp edges.+    DistManhattan+  | -- | Hybrid of Euclidean and Manhattan distances.+    DistHybrid   deriving (Generic, Read, Show, Eq, Ord, Enum, Bounded) +-- | What value to return from cellular noise evaluation.+--+-- These options allow for different visual effects by returning different+-- properties of the cell structure.+--+-- Distance-based results are not confined to @[-1, 1]@ under every metric —+-- 'DistManhattan' and 'DistHybrid' can exceed 1, matching FastNoiseLite. data CellularResult-  = CellValue-  | Distance-  | Distance2-  | Distance2Add-  | Distance2Sub-  | Distance2Mul-  | Distance2Div+  = -- | Return the hash value of the nearest cell point.+    -- Creates discrete regions with constant values.+    CellValue+  | -- | Return the distance to the nearest cell point.+    -- Creates a classic Worley noise pattern with cell boundaries.+    Distance+  | -- | Return the distance to the second-nearest cell point.+    -- Creates larger, more organic-looking cells.+    Distance2+  | -- | Return the sum of distances to the two nearest cell points.+    -- Creates smooth, rounded cells.+    Distance2Add+  | -- | Return the difference between distances to the two nearest cell points.+    -- Emphasizes cell boundaries and creates sharp edges.+    Distance2Sub+  | -- | Return the product of distances to the two nearest cell points.+    -- Creates cells with varying contrast.+    Distance2Mul+  | -- | Return the ratio of nearest to second-nearest distance.+    -- Creates normalized cell patterns.+    Distance2Div   deriving (Generic, Read, Show, Eq, Ord, Enum, Bounded)  distance :: (RealFrac a) => CellularDistanceFn -> a -> a -> a@@ -70,70 +113,149 @@   _ -> id {-# INLINE normDist #-} +distance3 :: (RealFrac a) => CellularDistanceFn -> a -> a -> a -> a+distance3 = \case+  DistEuclidean -> \ !x !y !z -> x * x + y * y + z * z+  DistEuclideanSq -> \ !x !y !z -> x * x + y * y + z * z+  DistManhattan -> \ !x !y !z -> abs x + abs y + abs z+  DistHybrid -> \ !x !y !z -> abs x + abs y + abs z + (x * x + y * y + z * z)+{-# INLINE distance3 #-}++-- | Fold the candidate cell points with the selector 'cellularResult' needs.+-- Shared by 'noise2' and 'noise3'; INLINE so the folds fuse with the callers'+-- point comprehensions (see the note on @points@ in 'noise2').+selectResult :: (RealFrac a, Floating a) => CellularResult -> CellularDistanceFn -> [(Hash, a)] -> a+selectResult res distFn points =+  let norm = normDist distFn+      coeff = 1 / (maxHash + 1)++      {-# INLINE selectMinHash #-}+      selectMinHash =+        let minHash (!hMin, !dMin) (!h, !d)+              | d < dMin = (h, d)+              | otherwise = (hMin, dMin)+         in foldl' minHash (0, infinity) points++      {-# INLINE selectMinDist #-}+      selectMinDist =+        let minDist !dMin (_, !d)+              | d < dMin = d+              | otherwise = dMin+         in foldl' minDist infinity points++      {-# INLINE selectSmallestTwo #-}+      selectSmallestTwo =+        let smallestTwo (!c, !d0, !d1) (!h, !d)+              | d < d0 = (h, d, d0)+              | d < d1 = (c, d0, d)+              | otherwise = (c, d0, d1)+         in foldl' smallestTwo (0, infinity, infinity) points+   in case res of+        CellValue ->+          let (!hash, !_) = selectMinHash+           in fromIntegral hash * coeff+        Distance ->+          let !d0 = selectMinDist+           in norm d0 - 1+        Distance2 ->+          let (!_, !_, !d1) = selectSmallestTwo+           in norm d1 - 1+        Distance2Add ->+          let (!_, !d0, !d1) = selectSmallestTwo+           in (norm d1 + norm d0) * 0.5 - 1+        Distance2Sub ->+          let (!_, !d0, !d1) = selectSmallestTwo+           in norm d1 - norm d0 - 1+        Distance2Mul ->+          let (!_, !d0, !d1) = selectSmallestTwo+           in norm d1 * norm d0 * 0.5 - 1+        Distance2Div ->+          let (!_, !d0, !d1) = selectSmallestTwo+           in norm d0 / norm d1 - 1+{-# INLINE selectResult #-}+ noise2 :: (RealFrac a, Floating a) => CellularConfig a -> Noise2 a-noise2 CellularConfig{..} =+noise2 CellularConfig{..} = mkNoise2 $ \ !seed !x !y ->   let !jitter = cellularJitter * 0.43701595-      !dist = distance cellularDistanceFn-      !norm = normDist cellularDistanceFn-      coeff = 1 / (fromIntegral (maxBound @Hash) + 1)-   in Noise2 $ \seed x y ->-        let (!hash, !d0u, !d1u) = noise2BaseWith jitter dist seed x y-            !d0 = norm d0u-            !d1 = norm d1u-         in case cellularResult of-              CellValue -> fromIntegral hash * coeff-              Distance -> d0 - 1-              Distance2 -> d1 - 1-              Distance2Add -> (d1 + d0) * 0.5 - 1-              Distance2Sub -> d1 - d0 - 1-              Distance2Mul -> d1 * d0 * 0.5 - 1-              Distance2Div -> d0 / d1 - 1-{-# INLINE noise2 #-}+      !rx = fastRound x+      !ry = fastRound y --- | Calculate 2D cellular noise values at a given point using the given distance function-noise2BaseWith-  :: (RealFrac a)-  => a-  -- ^ cellular jitter-  -> (a -> a -> a)-  -- ^ distance function-  -> Seed-  -> a-  -- ^ x-  -> a-  -- ^ y-  -> (Hash, a, a)-noise2BaseWith !jitter !dist !seed !x !y =-  foldl' @[]-    minmax-    (0, infinity, infinity)-    [pointDist (rx + xi) (ry + yi) | !xi <- [-1 .. 1], !yi <- [-1 .. 1]]- where-  !rx = round x-  !ry = round y+      dist = distance cellularDistanceFn -  minmax (!c, !d0, !d1) (!h, !d)-    | d < d0 = (h, d, d1')-    | otherwise = (c, d0, d1')-   where-    !d1' = max (min d1 d) d0+      {-# INLINE pointDist #-}+      pointDist !xi !yi =+        let !px = fromIntegral xi - x+            !py = fromIntegral yi - y+            !h = hash2 seed (primeX * xi) (primeY * yi)+            !i = h .&. 0x1FE+            !rvx = lookupRandVec2d i+            !rvy = lookupRandVec2d (i .|. 1)+            !d = dist (px + rvx * jitter) (py + rvy * jitter)+         in (h, d) -  pointDist !xi !yi =-    let !px = fromIntegral xi - x-        !py = fromIntegral yi - y-        !h = hash2 seed (primeX * xi) (primeY * yi)-        !i = h .&. 510-        !rvx = randVecs2d `U.unsafeIndex` fromIntegral i-        !rvy = randVecs2d `U.unsafeIndex` (fromIntegral i .|. 1)-        !d = dist (px + realToFrac rvx * jitter) (py + realToFrac rvy * jitter)-     in (h, d)-{-# INLINE noise2BaseWith #-}+      -- The [-1 .. 1] comprehension is load-bearing: enumFromTo takes part in+      -- foldr/build fusion with the folds below, so no list is ever built.+      -- OverloadedLists literals here would desugar to fromListN (no fusion),+      -- and hand-unrolled cons-chains defeat the fold's fusion entirely+      -- (measured ~5x slower). Same applies to the 3D comprehension.+      {-# INLINE points #-}+      points = [pointDist (rx + xi) (ry + yi) | !xi <- [-1 .. 1], !yi <- [-1 .. 1]]+   in selectResult cellularResult cellularDistanceFn points+{-# INLINE [2] noise2 #-} --- >>> U.length randVecs2d == 512+noise3 :: (RealFrac a, Floating a) => CellularConfig a -> Noise3 a+noise3 CellularConfig{..} = mkNoise3 $ \ !seed !x !y !z ->+  let !jitter = cellularJitter * 0.39614353+      !rx = fastRound x+      !ry = fastRound y+      !rz = fastRound z++      dist = distance3 cellularDistanceFn++      {-# INLINE pointDist #-}+      pointDist !xi !yi !zi =+        let !px = fromIntegral xi - x+            !py = fromIntegral yi - y+            !pz = fromIntegral zi - z+            !h = hash3 seed (primeX * xi) (primeY * yi) (primeZ * zi)+            !i = h .&. 0x3FC+            !rvx = lookupRandVec3d i+            !rvy = lookupRandVec3d (i .|. 1)+            !rvz = lookupRandVec3d (i .|. 2)+            !d = dist (px + rvx * jitter) (py + rvy * jitter) (pz + rvz * jitter)+         in (h, d)++      {-# INLINE points #-}+      points =+        [ pointDist (rx + xi) (ry + yi) (rz + zi)+        | !xi <- [-1 .. 1]+        , !yi <- [-1 .. 1]+        , !zi <- [-1 .. 1]+        ]+   in selectResult cellularResult cellularDistanceFn points+{-# INLINE [2] noise3 #-}++lookupRandVec2d :: (RealFrac a) => Hash -> a+lookupRandVec2d = realToFrac . indexPrimArray randVecs2dd . fromIntegral+{-# NOINLINE [1] lookupRandVec2d #-}++{-# RULES+"lookupRandVec2d/Float" forall h.+  lookupRandVec2d h =+    indexPrimArray randVecs2df (fromIntegral h)+"lookupRandVec2d/Double" forall h.+  lookupRandVec2d h =+    indexPrimArray randVecs2dd (fromIntegral h)+  #-}++randVecs2df :: PrimArray Float+randVecs2df = mapPrimArray realToFrac randVecs2dd++-- >>> sizeofPrimArray randVecs2dd == 512 -- True {- ORMOLU_DISABLE -}-randVecs2d :: U.Vector Float-randVecs2d =+randVecs2dd :: PrimArray Double+randVecs2dd =   [-0.2700222198,-0.9628540911,0.3863092627,-0.9223693152,0.04444859006,-0.999011673,-0.5992523158,-0.8005602176   ,-0.7819280288,0.6233687174,0.9464672271,0.3227999196,-0.6514146797,-0.7587218957,0.9378472289,0.347048376   ,-0.8497875957,-0.5271252623,-0.879042592,0.4767432447,-0.892300288,-0.4514423508,-0.379844434,-0.9250503802@@ -199,3 +321,155 @@   ,0.01426758847,-0.9998982128,-0.6734383991,0.7392433447,0.639412098,-0.7688642071,0.9211571421,0.3891908523   ,-0.146637214,-0.9891903394,-0.782318098,0.6228791163,-0.5039610839,-0.8637263605,-0.7743120191,-0.6328039957   ]++lookupRandVec3d :: (RealFrac a) => Hash -> a+lookupRandVec3d = realToFrac . indexPrimArray randVecs3dd . fromIntegral+{-# NOINLINE [1] lookupRandVec3d #-}++{-# RULES+"lookupRandVec3d/Float" forall h.+  lookupRandVec3d h =+    indexPrimArray randVecs3df (fromIntegral h)+"lookupRandVec3d/Double" forall h.+  lookupRandVec3d h =+    indexPrimArray randVecs3dd (fromIntegral h)+  #-}++randVecs3df :: PrimArray Float+randVecs3df = mapPrimArray realToFrac randVecs3dd++-- >>> sizeofPrimArray randVecs3dd == 1024+-- True+{- ORMOLU_DISABLE -}+randVecs3dd :: PrimArray Double+randVecs3dd =+  [-0.7292736885,-0.6618439697,0.1735581948,0,0.790292081,-0.5480887466,-0.2739291014,0+  ,0.7217578935,0.6226212466,-0.3023380997,0,0.565683137,-0.8208298145,-0.0790000257,0+  ,0.760049034,-0.5555979497,-0.3370999617,0,0.3713945616,0.5011264475,0.7816254623,0+  ,-0.1277062463,-0.4254438999,-0.8959289049,0,-0.2881560924,-0.5815838982,0.7607405838,0+  ,0.5849561111,-0.662820239,-0.4674352136,0,0.3307171178,0.0391653737,0.94291689,0+  ,0.8712121778,-0.4113374369,-0.2679381538,0,0.580981015,0.7021915846,0.4115677815,0+  ,0.503756873,0.6330056931,-0.5878203852,0,0.4493712205,0.601390195,0.6606022552,0+  ,-0.6878403724,0.09018890807,-0.7202371714,0,-0.5958956522,-0.6469350577,0.475797649,0+  ,-0.5127052122,0.1946921978,-0.8361987284,0,-0.9911507142,-0.05410276466,-0.1212153153,0+  ,-0.2149721042,0.9720882117,-0.09397607749,0,-0.7518650936,-0.5428057603,0.3742469607,0+  ,0.5237068895,0.8516377189,-0.02107817834,0,0.6333504779,0.1926167129,-0.7495104896,0+  ,-0.06788241606,0.3998305789,0.9140719259,0,-0.5538628599,-0.4729896695,-0.6852128902,0+  ,-0.7261455366,-0.5911990757,0.3509933228,0,-0.9229274737,-0.1782808786,0.3412049336,0+  ,-0.6968815002,0.6511274338,0.3006480328,0,0.9608044783,-0.2098363234,-0.1811724921,0+  ,0.06817146062,-0.9743405129,0.2145069156,0,-0.3577285196,-0.6697087264,-0.6507845481,0+  ,-0.1868621131,0.7648617052,-0.6164974636,0,-0.6541697588,0.3967914832,0.6439087246,0+  ,0.6993340405,-0.6164538506,0.3618239211,0,-0.1546665739,0.6291283928,0.7617583057,0+  ,-0.6841612949,-0.2580482182,-0.6821542638,0,0.5383980957,0.4258654885,0.7271630328,0+  ,-0.5026987823,-0.7939832935,-0.3418836993,0,0.3202971715,0.2834415347,0.9039195862,0+  ,0.8683227101,-0.0003762656404,-0.4959995258,0,0.791120031,-0.08511045745,0.6057105799,0+  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,0.8460043821,-0.3725217914,0.3814499973,0,0.8978727456,-0.1780209141,-0.4026575304,0+  ,0.2178065647,-0.9698322841,-0.1094789531,0,-0.1518031304,-0.7788918132,-0.6085091231,0+  ,-0.2600384876,-0.4755398075,-0.8403819825,0,0.572313509,-0.7474340931,-0.3373418503,0+  ,-0.7174141009,0.1699017182,-0.6756111411,0,-0.684180784,0.02145707593,-0.7289967412,0+  ,-0.2007447902,0.06555605789,-0.9774476623,0,-0.1148803697,-0.8044887315,0.5827524187,0+  ,-0.7870349638,0.03447489231,0.6159443543,0,-0.2015596421,0.6859872284,0.6991389226,0+  ,-0.08581082512,-0.10920836,-0.9903080513,0,0.5532693395,0.7325250401,-0.396610771,0+  ,-0.1842489331,-0.9777375055,-0.1004076743,0,0.0775473789,-0.9111505856,0.4047110257,0+  ,0.1399838409,0.7601631212,-0.6344734459,0,0.4484419361,-0.845289248,0.2904925424,0+  ]+{- ORMOLU_ENABLE -}
src/Numeric/Noise/Fractal.hs view
@@ -1,5 +1,5 @@ {-# LANGUAGE RecordWildCards #-}-{-# LANGUAGE Strict #-}+{-# LANGUAGE StrictData #-}  -- | -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com>@@ -37,14 +37,34 @@ import GHC.Generics import Numeric.Noise.Internal +-- | Configuration for fractal noise generation.+--+-- Fractal noise combines multiple octaves (layers) of noise at different+-- frequencies and amplitudes to create more complex, natural-looking patterns. data FractalConfig a = FractalConfig   { octaves :: Int+  -- ^ Number of noise layers to combine. More octaves create more detail+  -- but are more expensive to compute. Fewer than 1 octave produces+  -- constant 0.   , lacunarity :: a+  -- ^ Frequency multiplier between octaves. Each octave's frequency is+  -- the previous octave's frequency multiplied by lacunarity.   , gain :: a+  -- ^ Amplitude multiplier between octaves. Each octave's amplitude is+  -- the previous octave's amplitude multiplied by gain.+  -- Values \( < 1 \) create smoother noise, values \( > 1 \) create rougher noise.   , weightedStrength :: a+  -- ^ Controls how much each octave's amplitude is influenced by the+  -- previous octave's value. At 0 (the default), octaves have independent+  -- amplitudes. Range: \( [0, 1] \).+  --+  -- The weighting currently tracks the amplitude-scaled octave value, which+  -- diverges from FastNoiseLite — values near 1 can misbehave (e.g. inverted+  -- ridged octaves). It will align with FNL in 0.3.   }   deriving (Generic, Read, Show, Eq) +-- | Default configuration for fractal noise generation. defaultFractalConfig :: (RealFrac a) => FractalConfig a defaultFractalConfig =   FractalConfig@@ -53,23 +73,66 @@     , gain = 0.5     , weightedStrength = 0     }+{-# INLINEABLE defaultFractalConfig #-} +-- | Apply Fractal Brownian Motion (FBM) to a 2D noise function.+--+-- FBM combines multiple octaves of noise at increasing frequencies and+-- decreasing amplitudes to create natural-looking, multi-scale patterns.+-- This is the standard fractal noise implementation.+--+-- @+-- fbm :: Noise2 Float+-- fbm = fractal2 defaultFractalConfig perlin2+-- @ fractal2 :: (RealFrac a) => FractalConfig a -> Noise2 a -> Noise2 a-fractal2 config = Noise2 . fractal2With fractalNoiseMod (fractalAmpMod config) config . unNoise2-{-# INLINE fractal2 #-}+fractal2 config = mkNoise2 . fractal2With fractalNoiseMod (fractalAmpMod config) config . noise2At+{-# INLINE [2] fractal2 #-} +-- | Apply billow fractal to a 2D noise function.+--+-- Billow creates a cloud-like or billowy appearance by taking the absolute+-- value of each octave. This produces sharp ridges in the negative regions+-- of the noise, creating a distinct puffy or cloudy look.+--+-- @+-- clouds :: Noise2 Float+-- clouds = billow2 defaultFractalConfig perlin2+-- @ billow2 :: (RealFrac a) => FractalConfig a -> Noise2 a -> Noise2 a-billow2 config = Noise2 . fractal2With billowNoiseMod (billowAmpMod config) config . unNoise2-{-# INLINE billow2 #-}+billow2 config = mkNoise2 . fractal2With billowNoiseMod (billowAmpMod config) config . noise2At+{-# INLINE [2] billow2 #-} +-- | Apply ridged fractal to a 2D noise function.+--+-- Ridged creates sharp ridges by inverting and taking the absolute value+-- of each octave. This is particularly useful for terrain generation,+-- creating mountain ridges and valleys.+--+-- @+-- mountains :: Noise2 Float+-- mountains = ridged2 defaultFractalConfig perlin2+-- @ ridged2 :: (RealFrac a) => FractalConfig a -> Noise2 a -> Noise2 a-ridged2 config = Noise2 . fractal2With ridgedNoiseMod (ridgedAmpMod config) config . unNoise2-{-# INLINE ridged2 #-}+ridged2 config = mkNoise2 . fractal2With ridgedNoiseMod (ridgedAmpMod config) config . noise2At+{-# INLINE [2] ridged2 #-} +-- | Apply ping-pong fractal to a 2D noise function.+--+-- Ping-pong creates a wave-like pattern by folding the noise values back+-- and forth within a range, creating a distinctive undulating appearance.+-- The strength parameter controls the intensity of the ping-pong effect.+--+-- Output spans @[0, 1]@; it will align with FNL's @[-1, 1]@ in 0.3.+--+-- @+-- waves :: Noise2 Float+-- waves = pingPong2 defaultFractalConfig defaultPingPongStrength perlin2+-- @ pingPong2 :: (RealFrac a) => FractalConfig a -> PingPongStrength a -> Noise2 a -> Noise2 a pingPong2 config strength =-  Noise2 . fractal2With (pingPongNoiseMod strength) (pingPongAmpMod config) config . unNoise2-{-# INLINE pingPong2 #-}+  mkNoise2 . fractal2With (pingPongNoiseMod strength) (pingPongAmpMod config) config . noise2At+{-# INLINE [2] pingPong2 #-}  fractal2With   :: (RealFrac a)@@ -84,34 +147,46 @@   -> a   -> a fractal2With modNoise modAmps FractalConfig{..} noise2 seed x y-  | octaves < 1 = error "octaves must be a positive integer"+  | octaves < 1 = 0   | otherwise =-      let bounding = fractalBounding FractalConfig{..}+      let !bounding = fractalBounding FractalConfig{..}        in go octaves 0 seed 1 bounding  where-  go 0 acc _ _ _ = acc-  go o acc s freq amp =-    let noise = amp * modNoise (noise2 s (freq * x) (freq * y))-        amp' = amp * gain * modAmps (min (noise + 1) 2)+  go 0 !acc !_ !_ !_ = acc+  go !o !acc !s !freq !amp =+    let !noise = amp * modNoise (noise2 s (freq * x) (freq * y))+        !amp' = amp * gain * modAmps (min (noise + 1) 2)      in go (o - 1) (acc + noise) (s + 1) (freq * lacunarity) amp'-{-# INLINE fractal2With #-}+{-# INLINE [1] fractal2With #-} +-- | Apply Fractal Brownian Motion (FBM) to a 3D noise function.+--+-- 3D version of 'fractal2'. See 'fractal2' for details. fractal3 :: (RealFrac a) => FractalConfig a -> Noise3 a -> Noise3 a-fractal3 config = Noise3 . fractal3With fractalNoiseMod (fractalAmpMod config) config . unNoise3-{-# INLINE fractal3 #-}+fractal3 config = mkNoise3 . fractal3With fractalNoiseMod (fractalAmpMod config) config . noise3At+{-# INLINE [2] fractal3 #-} +-- | Apply billow fractal to a 3D noise function.+--+-- 3D version of 'billow2'. See 'billow2' for details. billow3 :: (RealFrac a) => FractalConfig a -> Noise3 a -> Noise3 a-billow3 config = Noise3 . fractal3With billowNoiseMod (billowAmpMod config) config . unNoise3-{-# INLINE billow3 #-}+billow3 config = mkNoise3 . fractal3With billowNoiseMod (billowAmpMod config) config . noise3At+{-# INLINE [2] billow3 #-} +-- | Apply ridged fractal to a 3D noise function.+--+-- 3D version of 'ridged2'. See 'ridged2' for details. ridged3 :: (RealFrac a) => FractalConfig a -> Noise3 a -> Noise3 a-ridged3 config = Noise3 . fractal3With ridgedNoiseMod (ridgedAmpMod config) config . unNoise3-{-# INLINE ridged3 #-}+ridged3 config = mkNoise3 . fractal3With ridgedNoiseMod (ridgedAmpMod config) config . noise3At+{-# INLINE [2] ridged3 #-} +-- | Apply ping-pong fractal to a 3D noise function.+--+-- 3D version of 'pingPong2'. See 'pingPong2' for details. pingPong3 :: (RealFrac a) => FractalConfig a -> PingPongStrength a -> Noise3 a -> Noise3 a pingPong3 config strength =-  Noise3 . fractal3With (pingPongNoiseMod strength) (pingPongAmpMod config) config . unNoise3-{-# INLINE pingPong3 #-}+  mkNoise3 . fractal3With (pingPongNoiseMod strength) (pingPongAmpMod config) config . noise3At+{-# INLINE [2] pingPong3 #-}  fractal3With   :: (RealFrac a)@@ -127,61 +202,98 @@   -> a   -> a fractal3With modNoise modAmps FractalConfig{..} noise3 seed x y z-  | octaves < 1 = error "octaves must be a positive integer"+  | octaves < 1 = 0   | otherwise =-      let bounding = fractalBounding FractalConfig{..}+      let !bounding = fractalBounding FractalConfig{..}        in go octaves 0 seed 1 bounding  where-  go 0 acc _ _ _ = acc-  go o acc s freq amp =-    let noise = amp * modNoise (noise3 s (freq * x) (freq * y) (freq * z))-        amp' = amp * gain * modAmps (min (noise + 1) 2)+  go 0 !acc !_ !_ !_ = acc+  go !o !acc !s !freq !amp =+    let !noise = amp * modNoise (noise3 s (freq * x) (freq * y) (freq * z))+        !amp' = amp * gain * modAmps (min (noise + 1) 2)      in go (o - 1) (acc + noise) (s + 1) (freq * lacunarity) amp'-{-# INLINE fractal3With #-}+{-# INLINE [1] fractal3With #-}  fractalBounding :: (RealFrac a) => FractalConfig a -> a-fractalBounding FractalConfig{..} =-  let amps = take octaves $ iterate (* gain) gain-   in 1 / (sum amps + 1)-{-# INLINE fractalBounding #-}+fractalBounding FractalConfig{..} = recip (sum amps + 1)+ where+  amps = take octaves $ iterate (* gain) gain+{-# INLINE [2] fractalBounding #-} +-- | Identity noise modifier for standard FBM.+--+-- This is used internally by 'fractal2' and 'fractal3'.+-- Exposed for users creating custom fractal implementations. fractalNoiseMod :: a -> a fractalNoiseMod = id {-# INLINE fractalNoiseMod #-}++-- | Amplitude modifier for standard FBM.+--+-- Uses the 'weightedStrength' parameter to influence amplitude based on+-- the previous octave's value. Exposed for custom fractal implementations. fractalAmpMod :: (Num a) => FractalConfig a -> a -> a fractalAmpMod FractalConfig{..} n = lerp 1 n weightedStrength {-# INLINE fractalAmpMod #-} +-- | Noise modifier for billow fractal.+--+-- Transforms noise value to @abs(n) * 2 - 1@, creating the billow effect.+-- Exposed for custom fractal implementations. billowNoiseMod :: (Num a) => a -> a billowNoiseMod n = abs n * 2 - 1 {-# INLINE billowNoiseMod #-} +-- | Amplitude modifier for billow fractal.+--+-- Uses the 'weightedStrength' parameter. Exposed for custom fractal implementations. billowAmpMod :: (Num a) => FractalConfig a -> a -> a billowAmpMod FractalConfig{..} n = lerp 1 n weightedStrength {-# INLINE billowAmpMod #-} +-- | Noise modifier for ridged fractal.+--+-- Transforms noise value to @abs(n) * (-2) + 1@, creating the ridge effect.+-- Exposed for custom fractal implementations. ridgedNoiseMod :: (Num a) => a -> a ridgedNoiseMod n = abs n * (-2) + 1 {-# INLINE ridgedNoiseMod #-} +-- | Amplitude modifier for ridged fractal.+--+-- Uses the 'weightedStrength' parameter with inverted noise value.+-- Exposed for custom fractal implementations. ridgedAmpMod :: (Num a) => FractalConfig a -> a -> a ridgedAmpMod FractalConfig{..} n = lerp 1 (1 - n) weightedStrength {-# INLINE ridgedAmpMod #-} +-- | Strength parameter for ping-pong fractal noise.+--+-- Controls the intensity of the ping-pong folding effect.+-- Higher values create more frequent oscillations. newtype PingPongStrength a = PingPongStrength a   deriving (Generic) +-- | Default ping-pong strength value. defaultPingPongStrength :: (RealFrac a) => PingPongStrength a defaultPingPongStrength = PingPongStrength 2 {-# INLINE defaultPingPongStrength #-} +-- | Noise modifier for ping-pong fractal.+--+-- Folds noise values back and forth within a range, creating a wave-like+-- pattern. The strength parameter controls the folding intensity.+-- Exposed for custom fractal implementations. pingPongNoiseMod :: (RealFrac a) => PingPongStrength a -> a -> a pingPongNoiseMod (PingPongStrength s) n =   let n' = (n + 1) * s       t = n' - fromIntegral @Int (truncate (n' * 0.5) * 2)-   in if t < 1 then t else 2 - t+   in 1 - abs (t - 1) {-# INLINE pingPongNoiseMod #-} +-- | Amplitude modifier for ping-pong fractal.+--+-- Uses the 'weightedStrength' parameter. Exposed for custom fractal implementations. pingPongAmpMod :: (Num a) => FractalConfig a -> a -> a pingPongAmpMod FractalConfig{..} n = lerp 1 n weightedStrength {-# INLINE pingPongAmpMod #-}
src/Numeric/Noise/Internal.hs view
@@ -3,14 +3,33 @@ -- Stability : experimental module Numeric.Noise.Internal (   module Math,-  Noise2 (..),+  Noise (..),+  constant,+  remap,+  warp,+  reseed,+  blend,+  sliceX2,+  sliceY2,+  sliceX3,+  sliceY3,+  sliceZ3,+  Noise1',+  Noise1,+  mkNoise1,+  noise1At,+  Noise2',+  Noise2,+  mkNoise2,+  noise2At,   next2,-  map2,   clamp2,   const2,-  Noise3 (..),+  Noise3',+  Noise3,+  mkNoise3,+  noise3At,   next3,-  map3,   clamp3,   const3, ) where@@ -25,138 +44,355 @@   quinticInterp,  ) -newtype Noise2 a = Noise2-  {unNoise2 :: Seed -> a -> a -> a}+-- |  'Noise' represents a function from a 'Seed' and coordinates @p@ to a noise+-- value @v@.+--+-- For convenience, dimension-specific type aliases are provided: 'Noise1',+-- 'Noise2', and 'Noise3', plus primed variants that separate the coordinate+-- and value types.+--+-- Use 'warp' to transform coordinates and 'remap' (or 'fmap') to transform values.+--+-- To evaluate noise functions, use 'noise1At', 'noise2At', or 'noise3At'.+--+-- NB: 'Noise' is a lawful 'Profunctor' where 'lmap' = warp and 'rmap' = remap.+-- There are some useful implications to this, but pure-noise is committed to+-- a minimal dependency footprint and so will not provide this instance itself.+--+-- === __Algebraic composition__+--+-- 'Noise' can be composed algebraically:+--+-- @+-- combined :: Noise (Float, Float) Float+-- combined = (perlin2 + superSimplex2) / 2+-- @+--+-- === __Coordinate Transformation__+--+-- This allows you to, for example, compose multiple layers of noise at different+-- offsets.+--+-- @+-- scaled :: Noise2 Float+-- scaled = warp (\\(x, y) -> (x * 2, y * 2)) perlin2+-- @+newtype Noise p v = Noise {unNoise :: Seed -> p -> v} +-- NOTE: Noise p v is isomorphic to Reader (Seed, p), so it has trivial+-- instances of Monad and Category, Arrow, ArrowChoice, ArrowApply, etc.+--+-- I've decided not to include Category et al. as instances for now+-- because I can't come up with a use-case that is not sufficiently+-- covered by the monad instance.++-- | Noise admits 'Functor' on the value it produces+instance Functor (Noise p) where+  fmap f (Noise g) = Noise (\seed -> f . g seed)++-- | Noise admits 'Applicative' on the value it produces+instance Applicative (Noise p) where+  pure a = Noise $ \_ _ -> a+  liftA2 f (Noise g) (Noise h) = Noise (\s p -> g s p `f` h s p)++-- | Note: The 'Monad' instance evaluates all noise functions at the same+-- seed and coordinate. For independent sampling at different coordinates,+-- use 'warp' to transform the coordinate space.+--+-- @+-- do n1 <- perlin2+--    n2 <- superSimplex2+--    return (n1 + n2)+-- @+--+-- is equivalent to:+--+-- @+-- perlin2 + superSimplex2+-- @+--+-- This is useful for domain warping.+instance Monad (Noise p) where+  Noise g >>= f = Noise (\s p -> unNoise (f (g s p)) s p)++instance (Num a) => Num (Noise p a) where+  (+) = liftA2 (+)+  (*) = liftA2 (*)+  abs = fmap abs+  signum = fmap signum+  fromInteger i = pure (fromInteger i)+  negate = fmap negate++instance (Fractional a) => Fractional (Noise p a) where+  fromRational = pure . fromRational+  recip = fmap recip+  (/) = liftA2 (/)++instance (Floating a) => Floating (Noise p a) where+  pi = pure pi+  exp = fmap exp+  log = fmap log+  sin = fmap sin+  cos = fmap cos+  asin = fmap asin+  acos = fmap acos+  atan = fmap atan+  sinh = fmap sinh+  cosh = fmap cosh+  asinh = fmap asinh+  acosh = fmap acosh+  atanh = fmap atanh++-- | 1D noise: a single coordinate of type @p@ producing values of type @v@.+type Noise1' p v = Noise p v++-- | 1D noise with a single type for coordinates and values.+type Noise1 v = Noise1' v v++-- | Build a 1D noise function from a plain @seed -> coordinate -> value@+-- function. Inverse of 'noise1At'.+mkNoise1 :: (Seed -> p -> v) -> Noise1' p v+mkNoise1 = Noise+{-# INLINE mkNoise1 #-}++-- | Evaluate a 1D noise function at the given coordinates with the given seed.+-- Currently, you must use a slicing function like 'sliceX2' to reduce+-- higher-dimensional noise into 1D noise.+noise1At :: Noise1 a -> Seed -> a -> a+noise1At = unNoise+{-# INLINE noise1At #-}++-- | 2D noise: a pair of coordinates of type @p@ producing values of type @v@.+type Noise2' p v = Noise (p, p) v++-- | 2D noise with a single type for coordinates and values.+type Noise2 v = Noise2' v v++-- | Build a 2D noise function from a plain @seed -> x -> y -> value@+-- function. Inverse of 'noise2At'.+mkNoise2 :: (Seed -> p -> p -> v) -> Noise2' p v+mkNoise2 f = Noise (\s (x, y) -> f s x y)+{-# INLINE mkNoise2 #-}++-- | Evaluate a 2D noise function at the given coordinates with the given seed.+noise2At+  :: Noise2 a+  -> Seed+  -- ^ deterministic seed+  -> a+  -- ^ x coordinate+  -> a+  -- ^ y coordinate+  -> a+noise2At (Noise f) seed x y = f seed (x, y)+{-# INLINE noise2At #-}++-- | 3D noise: a triple of coordinates of type @p@ producing values of type @v@.+type Noise3' p v = Noise (p, p, p) v++-- | 3D noise with a single type for coordinates and values.+type Noise3 v = Noise3' v v++-- | Build a 3D noise function from a plain @seed -> x -> y -> z -> value@+-- function. Inverse of 'noise3At'.+mkNoise3 :: (Seed -> p -> p -> p -> v) -> Noise3' p v+mkNoise3 f = Noise (\s (x, y, z) -> f s x y z)+{-# INLINE mkNoise3 #-}++-- | Evaluate a 3D noise function at the given coordinates with the given seed.+noise3At+  :: Noise3 a+  -> Seed+  -- ^ deterministic seed+  -> a+  -- ^ x coordinate+  -> a+  -- ^ y coordinate+  -> a+  -- ^ z coordinate+  -> a+noise3At (Noise f) seed x y z = f seed (x, y, z)+{-# INLINE noise3At #-}++-- | Transform the values produced by a noise function.+--+-- This is an alias for 'fmap'. Use it to transform noise values after generation:+--+-- === __Examples__+--+-- @+-- -- Scale noise from [-1, 1] to [0, 1]+-- normalized :: Noise2 Float+-- normalized = remap (\\x -> (x + 1) / 2) perlin2+-- @+remap :: (a -> b) -> Noise p a -> Noise p b+remap = fmap+{-# INLINE remap #-}++-- | Transform the coordinate space of a noise function.+--+-- This allows you to scale, rotate, or otherwise modify coordinates before+-- they're passed to the noise function:+--+-- NB: This is 'Data.Functor.Contravariant.contramap'+--+-- === __Examples__+--+-- @+-- -- Scale the noise frequency+-- scaled :: Noise2 Float+-- scaled = warp (\\(x, y) -> (x * 2, y * 2)) perlin2+--+-- -- Rotate the noise field+-- rotated :: Noise2 Float+-- rotated = warp (\\(x, y) -> (x * cos a - y * sin a, x * sin a + y * cos a)) perlin2+--   where a = pi / 4+-- @+warp :: (p -> p') -> Noise p' v -> Noise p v+warp f (Noise g) = Noise (\s p -> g s (f p))+{-# INLINE warp #-}++-- | Modify the seed used by a noise function.+--+-- This is useful for generating independent layers of noise:+--+-- See also 'next2' and 'next3' for convenient increment-by-one variants.+--+-- === __Examples__+-- @+-- layer1 = perlin2+-- layer2 = reseed (+1) perlin2+-- layer3 = reseed (+2) perlin2+--+-- combined = (layer1 + layer2 + layer3) / 3+-- @+reseed :: (Seed -> Seed) -> Noise p a -> Noise p a+reseed f (Noise g) = Noise (g . f)+{-# INLINE reseed #-}++constant :: a -> Noise c a+constant = pure+{-# INLINE constant #-}++-- | Combine two noise functions with a custom blending function.+--+-- This is an alias for 'liftA2'. Use it to mix multiple noise sources:+--+-- @+-- -- Multiply two noise functions+-- multiplied :: Noise2 Float+-- multiplied = blend (*) perlin2 superSimplex2+--+-- -- Custom blending based on values+-- custom :: Noise2 Float+-- custom = blend (\\a b -> if a > 0 then a else b) perlin2 superSimplex2+-- @+blend :: (a -> b -> c) -> Noise p a -> Noise p b -> Noise p c+blend = liftA2+{-# INLINE blend #-}++-- | Clamp a noise function between the given lower and higher bound+clampNoise :: (Ord a) => a -> a -> Noise p a -> Noise p a+clampNoise l u = fmap (clamp l u)+{-# INLINE clampNoise #-}++-- | Slice a 2D noise function at a fixed X coordinate to produce 1D noise.+--+-- === __Examples__+--+-- @+-- noise1d :: Noise1 Float+-- noise1d = sliceX2 0.0 perlin2  -- Fix X at 0, vary Y+--+-- -- Evaluate at Y = 5.0+-- value = noise1At noise1d seed 5.0+-- @+sliceX2 :: p -> Noise2' p v -> Noise1' p v+sliceX2 x = warp (x,)+{-# INLINE sliceX2 #-}++-- | Slice a 2D noise function at a fixed Y coordinate to produce 1D noise.+--+-- === __Examples__+--+-- @+-- noise1d :: Noise1 Float+-- noise1d = sliceY2 0.0 perlin2  -- Fix Y at 0, vary X+--+-- -- Evaluate at X = 5.0+-- value = noise1At noise1d seed 5.0+-- @+sliceY2 :: p -> Noise2' p v -> Noise1' p v+sliceY2 y = warp (,y)+{-# INLINE sliceY2 #-}++-- | Slice a 3D noise function at a fixed X coordinate to produce 2D noise.+--+-- === __Examples__+--+-- @+-- noise2d :: Noise2 Float+-- noise2d = sliceX3 0.0 perlin3  -- Fix X at 0, vary Y and Z+--+-- -- Evaluate at Y = 1.0, Z = 2.0+-- value = noise2At noise2d seed 1.0 2.0+-- @+sliceX3 :: p -> Noise3' p v -> Noise2' p v+sliceX3 x = warp (\(y, z) -> (x, y, z))+{-# INLINE sliceX3 #-}++-- | Slice a 3D noise function at a fixed Y coordinate to produce 2D noise.+--+-- === __Examples__+--+-- @+-- noise2d :: Noise2 Float+-- noise2d = sliceY3 0.0 perlin3  -- Fix Y at 0, vary X and Z+-- @+sliceY3 :: p -> Noise3' p v -> Noise2' p v+sliceY3 y = warp (\(x, z) -> (x, y, z))+{-# INLINE sliceY3 #-}++-- | Slice a 3D noise function at a fixed Z coordinate to produce 2D noise.+--+-- This is useful for extracting 2D slices from 3D noise at different heights:+--+-- === __Examples__+--+-- @+-- heightmap :: Noise2 Float+-- heightmap = sliceZ3 10.0 perlin3  -- Sample at Z = 10+-- @+sliceZ3 :: p -> Noise3' p v -> Noise2' p v+sliceZ3 z = warp (\(x, y) -> (x, y, z))+{-# INLINE sliceZ3 #-}++-- | Increment the seed for a 2D noise function. See 'reseed'. next2 :: Noise2 a -> Noise2 a-next2 (Noise2 f) = Noise2 (\s x y -> f (s + 1) x y)+next2 = reseed (+ 1) {-# INLINE next2 #-} -map2 :: (a -> a) -> Noise2 a -> Noise2 a-map2 f (Noise2 g) = Noise2 (\s x y -> f (g s x y))-{-# INLINE map2 #-}-+-- | Clamp the output of a 2D noise function to the range @[lower, upper]@. clamp2 :: (Ord a) => a -> a -> Noise2 a -> Noise2 a-clamp2 l u (Noise2 f) = Noise2 $ \s x y -> clamp l u (f s x y)+clamp2 = clampNoise {-# INLINE clamp2 #-} +-- | A noise function that produces the same value everywhere. Alias of 'pure'. const2 :: a -> Noise2 a-const2 a = Noise2 (\_ _ _ -> a)+const2 = pure {-# INLINE const2 #-} -instance (Num a) => Num (Noise2 a) where-  Noise2 f + Noise2 g = Noise2 $ \s x y -> f s x y + g s x y-  {-# INLINE (+) #-}-  Noise2 f * Noise2 g = Noise2 $ \s x y -> f s x y * g s x y-  {-# INLINE (*) #-}-  abs (Noise2 f) = Noise2 $ \s x y -> abs (f s x y)-  {-# INLINE abs #-}-  signum (Noise2 f) = Noise2 $ \s x y -> signum (f s x y)-  {-# INLINE signum #-}-  fromInteger i = const2 (fromInteger i)-  {-# INLINE fromInteger #-}-  negate (Noise2 f) = Noise2 $ \s x y -> negate (f s x y)-  {-# INLINE negate #-}--instance (Fractional a) => Fractional (Noise2 a) where-  fromRational r = const2 (fromRational r)-  {-# INLINE fromRational #-}-  recip (Noise2 f) = Noise2 $ \s x y -> recip (f s x y)-  {-# INLINE recip #-}-  Noise2 f / Noise2 g = Noise2 $ \s x y -> f s x y / g s x y-  {-# INLINE (/) #-}--instance (Floating a) => Floating (Noise2 a) where-  pi = const2 pi-  {-# INLINE pi #-}-  exp (Noise2 f) = Noise2 $ \s x y -> exp (f s x y)-  {-# INLINE exp #-}-  log (Noise2 f) = Noise2 $ \s x y -> log (f s x y)-  {-# INLINE log #-}-  sin (Noise2 f) = Noise2 $ \s x y -> sin (f s x y)-  {-# INLINE sin #-}-  cos (Noise2 f) = Noise2 $ \s x y -> cos (f s x y)-  {-# INLINE cos #-}-  asin (Noise2 f) = Noise2 $ \s x y -> asin (f s x y)-  {-# INLINE asin #-}-  acos (Noise2 f) = Noise2 $ \s x y -> acos (f s x y)-  {-# INLINE acos #-}-  atan (Noise2 f) = Noise2 $ \s x y -> atan (f s x y)-  {-# INLINE atan #-}-  sinh (Noise2 f) = Noise2 $ \s x y -> sinh (f s x y)-  {-# INLINE sinh #-}-  cosh (Noise2 f) = Noise2 $ \s x y -> cosh (f s x y)-  {-# INLINE cosh #-}-  asinh (Noise2 f) = Noise2 $ \s x y -> asinh (f s x y)-  {-# INLINE asinh #-}-  acosh (Noise2 f) = Noise2 $ \s x y -> acosh (f s x y)-  {-# INLINE acosh #-}-  atanh (Noise2 f) = Noise2 $ \s x y -> atanh (f s x y)-  {-# INLINE atanh #-}--newtype Noise3 a = Noise3-  {unNoise3 :: Seed -> a -> a -> a -> a}-+-- | Increment the seed for a 3D noise function. See 'reseed'. next3 :: Noise3 a -> Noise3 a-next3 (Noise3 f) = Noise3 (\s x y z -> f (s + 1) x y z)+next3 = reseed (+ 1) {-# INLINE next3 #-} -map3 :: (a -> a) -> Noise3 a -> Noise3 a-map3 f (Noise3 g) = Noise3 (\s x y z -> f (g s x y z))-{-# INLINE map3 #-}-+-- | A noise function that produces the same value everywhere. Alias of 'pure'. const3 :: a -> Noise3 a-const3 a = Noise3 (\_ _ _ _ -> a)+const3 = pure {-# INLINE const3 #-} +-- | Clamp the output of a 3D noise function to the range @[lower, upper]@. clamp3 :: (Ord a) => a -> a -> Noise3 a -> Noise3 a-clamp3 l u (Noise3 f) = Noise3 $ \s x y z -> clamp l u (f s x y z)+clamp3 = clampNoise {-# INLINE clamp3 #-}--instance (Num a) => Num (Noise3 a) where-  Noise3 f + Noise3 g = Noise3 $ \s x y z -> f s x y z + g s x y z-  {-# INLINE (+) #-}-  Noise3 f * Noise3 g = Noise3 $ \s x y z -> f s x y z * g s x y z-  {-# INLINE (*) #-}-  abs (Noise3 f) = Noise3 $ \s x y z -> abs (f s x y z)-  {-# INLINE abs #-}-  signum (Noise3 f) = Noise3 $ \s x y z -> signum (f s x y z)-  {-# INLINE signum #-}-  fromInteger i = const3 (fromInteger i)-  {-# INLINE fromInteger #-}-  negate (Noise3 f) = Noise3 $ \s x y z -> negate (f s x y z)-  {-# INLINE negate #-}--instance (Fractional a) => Fractional (Noise3 a) where-  fromRational r = const3 (fromRational r)-  {-# INLINE fromRational #-}-  recip (Noise3 f) = Noise3 $ \s x y z -> recip (f s x y z)-  {-# INLINE recip #-}--instance (Floating a) => Floating (Noise3 a) where-  pi = const3 pi-  {-# INLINE pi #-}-  exp (Noise3 f) = Noise3 $ \s x y z -> exp (f s x y z)-  {-# INLINE exp #-}-  log (Noise3 f) = Noise3 $ \s x y z -> log (f s x y z)-  {-# INLINE log #-}-  sin (Noise3 f) = Noise3 $ \s x y z -> sin (f s x y z)-  {-# INLINE sin #-}-  cos (Noise3 f) = Noise3 $ \s x y z -> cos (f s x y z)-  {-# INLINE cos #-}-  asin (Noise3 f) = Noise3 $ \s x y z -> asin (f s x y z)-  {-# INLINE asin #-}-  acos (Noise3 f) = Noise3 $ \s x y z -> acos (f s x y z)-  {-# INLINE acos #-}-  atan (Noise3 f) = Noise3 $ \s x y z -> atan (f s x y z)-  {-# INLINE atan #-}-  sinh (Noise3 f) = Noise3 $ \s x y z -> sinh (f s x y z)-  {-# INLINE sinh #-}-  cosh (Noise3 f) = Noise3 $ \s x y z -> cosh (f s x y z)-  {-# INLINE cosh #-}-  asinh (Noise3 f) = Noise3 $ \s x y z -> asinh (f s x y z)-  {-# INLINE asinh #-}-  acosh (Noise3 f) = Noise3 $ \s x y z -> acosh (f s x y z)-  {-# INLINE acosh #-}-  atanh (Noise3 f) = Noise3 $ \s x y z -> atanh (f s x y z)-  {-# INLINE atanh #-}
src/Numeric/Noise/Internal/Math.hs view
@@ -12,6 +12,7 @@   hermiteInterp,   quinticInterp,   clamp,+  fastRound,   primeX,   primeY,   primeZ,@@ -20,6 +21,7 @@   infinity,   g2,   sqrt3,+  rotate3,   valCoord2,   valCoord3,   gradCoord2,@@ -28,14 +30,28 @@ ) where  import Data.Bits+import Data.Bool (bool) import Data.Int-import Data.Vector.Unboxed qualified as U+import Data.Primitive.PrimArray import Data.Word +-- | Seed value for deterministic noise generation.+--+-- Using the same 'Seed' value will produce the same noise pattern,+-- allowing for reproducible results. Different seed values produce+-- different, independent noise patterns.+--+-- Only the low 32 bits participate in hashing (matching FastNoiseLite's+-- @int@ seed): seeds that differ only in their upper 32 bits generate+-- identical noise. type Seed = Word64++-- | Internal hash value type used in noise calculations. type Hash = Int32 --- | monotonic lerp+-- | Linear interpolation between two values.+--+-- Monotonic lerp lerp   :: (Num a)   => a@@ -46,25 +62,97 @@   -- ^ parameter in range [0, 1]   -> a lerp v0 v1 t = v0 + t * (v1 - v0)-{-# INLINE lerp #-}+{-# INLINE [1] lerp #-} --- | cubic interpolation+{-# RULES+"lerp/Float/0" forall (a :: Float) b.+  lerp a b 0 =+    a+"lerp/Double/0" forall (a :: Double) b.+  lerp a b 0 =+    a+"lerp/Float/1" forall (a :: Float) b.+  lerp a b 1 =+    b+"lerp/Double/1" forall (a :: Double) b.+  lerp a b 1 =+    b+"lerp/id" forall a t. lerp a a t = a+"lerp/compose/start" forall a b t u.+  lerp (lerp a b u) b t =+    lerp a b (u + t - t * u)+"lerp/compose/end" forall a b t u.+  lerp a (lerp a b u) t =+    lerp a b (t * u)+  #-}++-- | Cubic interpolation through four control points. cubicInterp :: (Num a) => a -> a -> a -> a -> a -> a-cubicInterp a b c d t =-  let !p = (d - c) - (a - b)-   in t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b-{-# INLINE cubicInterp #-}+cubicInterp a !b c d !t =+  let !c' = c - a+      !a' = a - b+      !p = (d - c) - a'+      !b' = a' - p+   in b + t * (c' + t * (b' + t * p))+{-# INLINE [1] cubicInterp #-} --- | hermite interpolation+{-# RULES+"cubicInterp/Float/0" forall (a :: Float) b c d.+  cubicInterp a b c d 0 =+    b+"cubicInterp/Double/0" forall (a :: Double) b c d.+  cubicInterp a b c d 0 =+    b+"cubicInterp/Float/1" forall (a :: Float) b c d.+  cubicInterp a b c d 1 =+    c+"cubicInterp/Double/1" forall (a :: Double) b c d.+  cubicInterp a b c d 1 =+    c+"cubicInterp/Float/0.5" forall (a :: Float) b c d.+  cubicInterp a b c d (0.5 :: Float) =+    0.125 * (-a + 5 * b + 5 * c - d)+"cubicInterp/Double/0.5" forall (a :: Double) b c d.+  cubicInterp a b c d (0.5 :: Double) =+    0.125 * (-a + 5 * b + 5 * c - d)+  #-}++-- | Hermite interpolation curve (smoothstep). hermiteInterp :: (Num a) => a -> a hermiteInterp t = t * t * (3 - 2 * t)-{-# INLINE hermiteInterp #-}+{-# INLINE [1] hermiteInterp #-} --- | quintic interpolation+{-# RULES+"hermiteInterp/Float/0" hermiteInterp (0 :: Float) = 0+"hermiteInterp/Double/0" hermiteInterp (0 :: Double) = 0+"hermiteInterp/Float/1" hermiteInterp (1 :: Float) = 1+"hermiteInterp/Double/1" hermiteInterp (1 :: Double) = 1+  #-}++-- | Quintic interpolation curve (smootherstep). quinticInterp :: (Num a) => a -> a quinticInterp t = t * t * t * (t * (t * 6 - 15) + 10)-{-# INLINE quinticInterp #-}+{-# INLINE [1] quinticInterp #-} +{-# RULES+"quinticInterp/Float/0"+  quinticInterp (0 :: Float) =+    0+"quinticInterp/Double/0"+  quinticInterp (0 :: Double) =+    0+"quinticInterp/Float/1"+  quinticInterp (1 :: Float) =+    1+"quinticInterp/Double/1"+  quinticInterp (1 :: Double) =+    1+  #-}++-- | Clamp a value to a specified range.+--+-- Returns the value if it's within bounds, otherwise returns+-- the nearest boundary. clamp   :: (Ord a)   => a@@ -74,12 +162,18 @@   -> a   -- ^ value   -> a-clamp l u v-  | v < l = l-  | v > u = u-  | otherwise = v+clamp l u v = min (max v l) u {-# INLINE clamp #-} +-- | Round half away from zero, matching FastNoiseLite's @FastRound@.+--+-- 'round' rounds half to even and, more importantly, GHC lowers it to an+-- @rintFloat@ FFI call that dominates hot loops; 'truncate' compiles to an+-- inline @float2Int#@.+fastRound :: (RealFrac a) => a -> Hash+fastRound v = truncate (v + bool (-0.5) 0.5 (v >= 0))+{-# INLINE fastRound #-}+ primeX, primeY, primeZ :: Hash primeX = 501125321 {-# INLINE primeX #-}@@ -112,48 +206,73 @@ sqrt3 = 1.7320508075688772935274463415059 {-# INLINE sqrt3 #-} -valCoord2 :: (RealFrac a) => Word64 -> Hash -> Hash -> a+-- | Rotation for OpenSimplex2\/2S+rotate3 :: (Fractional a) => a -> a -> a -> (a, a, a)+rotate3 xo yo zo =+  let !r = (xo + yo + zo) * (2 / 3)+   in (r - xo, r - yo, r - zo)+{-# INLINE rotate3 #-}++valCoord2 :: (RealFrac a) => Seed -> Hash -> Hash -> a valCoord2 seed xPrimed yPrimed =   let !hash = hash2 seed xPrimed yPrimed       !val = (hash * hash) `xor` (hash `shiftL` 19)-   in fromIntegral val / maxHash+   in fromIntegral val * recip (maxHash + 1) {-# INLINE valCoord2 #-} -valCoord3 :: (RealFrac a) => Word64 -> Hash -> Hash -> Hash -> a+valCoord3 :: (RealFrac a) => Seed -> Hash -> Hash -> Hash -> a valCoord3 seed xPrimed yPrimed zPrimed =   let !hash = hash3 seed xPrimed yPrimed zPrimed       !val = (hash * hash) `xor` (hash `shiftL` 19)-   in fromIntegral val / maxHash+   in fromIntegral val * recip (maxHash + 1) {-# INLINE valCoord3 #-}  gradCoord2 :: (RealFrac a) => Seed -> Hash -> Hash -> a -> a -> a gradCoord2 seed xPrimed yPrimed xd yd =   let !hash = hash2 seed xPrimed yPrimed       !ix = (hash `xor` (hash `shiftR` 15)) .&. 0xFE-      !xg = grad2d `U.unsafeIndex` fromIntegral ix-      !yg = grad2d `U.unsafeIndex` fromIntegral (ix .|. 1)-   in xd * realToFrac xg + yd * realToFrac yg-{-# INLINE gradCoord2 #-}+      !xg = lookupGrad2 ix+      !yg = lookupGrad2 (ix .|. 1)+   in xd * xg + yd * yg+-- Phase 2 inlining ensures specialization happens after hash computation+-- but before gradient lookup, allowing REWRITE RULES to fire effectively+{-# INLINE [2] gradCoord2 #-}  gradCoord3 :: (RealFrac a) => Seed -> Hash -> Hash -> Hash -> a -> a -> a -> a gradCoord3 seed xPrimed yPrimed zPrimed xd yd zd =   let !hash = hash3 seed xPrimed yPrimed zPrimed       !ix = (hash `xor` (hash `shiftR` 15)) .&. 0xFC-      !xg = grad3d `U.unsafeIndex` fromIntegral ix-      !yg = grad3d `U.unsafeIndex` fromIntegral (ix .|. 1)-      !zg = grad3d `U.unsafeIndex` fromIntegral (ix .|. 2)-   in xd * fromIntegral xg + yd * fromIntegral yg + zd * fromIntegral zg+      !xg = lookupGrad3 ix+      !yg = lookupGrad3 (ix .|. 1)+      !zg = lookupGrad3 (ix .|. 2)+   in xd * xg + yd * yg + zd * zg {-# INLINE gradCoord3 #-}  maxHash :: (RealFrac a) => a-maxHash = realToFrac (maxBound @Hash)+maxHash = fromIntegral (maxBound @Hash) {-# INLINE maxHash #-} +lookupGrad2 :: (RealFrac a) => Hash -> a+lookupGrad2 = realToFrac . (grad2dd `indexPrimArray`) . fromIntegral+{-# INLINE [0] lookupGrad2 #-}++{-# RULES+"lookupGrad2/Float" forall (i :: Hash).+  lookupGrad2 i =+    indexPrimArray grad2df (fromIntegral i)+"lookupGrad2/Double" forall (i :: Hash).+  lookupGrad2 i =+    indexPrimArray grad2dd (fromIntegral i)+  #-}++grad2df :: PrimArray Float+grad2df = mapPrimArray realToFrac grad2dd+ {- ORMOLU_DISABLE -}--- >>> U.length grad2d == 256+-- >>> sizeofPrimArray grad2d == 256 -- True-grad2d :: U.Vector Float-grad2d =+grad2dd :: PrimArray Double+grad2dd =   [ 0.130526192220052,  0.99144486137381 ,  0.38268343236509 ,  0.923879532511287,  0.608761429008721,  0.793353340291235,  0.793353340291235,  0.608761429008721,     0.923879532511287,  0.38268343236509 ,  0.99144486137381 ,  0.130526192220051,  0.99144486137381 , -0.130526192220051,  0.923879532511287, -0.38268343236509,     0.793353340291235, -0.60876142900872 ,  0.608761429008721, -0.793353340291235,  0.38268343236509 , -0.923879532511287,  0.130526192220052, -0.99144486137381,@@ -188,10 +307,29 @@    -0.38268343236509 , -0.923879532511287, -0.923879532511287, -0.38268343236509 , -0.923879532511287,  0.38268343236509 , -0.38268343236509 ,  0.923879532511287   ] --- >>> U.length grad3d == 256+{- ORMOLU_ENABLE -}++lookupGrad3 :: (RealFrac a) => Hash -> a+lookupGrad3 = realToFrac . (grad3dd `indexPrimArray`) . fromIntegral+{-# INLINE [0] lookupGrad3 #-}++{-# RULES+"lookupGrad3/Float" forall (i :: Hash).+  lookupGrad3 i =+    indexPrimArray grad3df (fromIntegral i)+"lookupGrad3/Double" forall (i :: Hash).+  lookupGrad3 i =+    indexPrimArray grad3dd (fromIntegral i)+  #-}++grad3df :: PrimArray Float+grad3df = mapPrimArray realToFrac grad3dd++{- ORMOLU_DISABLE -}+-- >>> sizeofPrimArray grad3d == 256 -- True-grad3d :: U.Vector Int-grad3d =+grad3dd :: PrimArray Double+grad3dd =   [ 0, 1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0   , 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0   , 1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0
src/Numeric/Noise/OpenSimplex.hs view
@@ -1,5 +1,3 @@-{-# LANGUAGE Strict #-}- -- | -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com> -- Stability: experimental@@ -9,78 +7,149 @@   -- * 2D Noise   noise2,   noise2Base,++  -- * 3D Noise+  noise3,+  noise3Base, ) where +import Data.Bits (complement, shiftR, (.&.))+import Data.Bool (bool) import Numeric.Noise.Internal import Numeric.Noise.Internal.Math  noise2 :: (RealFrac a) => Noise2 a-noise2 = Noise2 noise2Base+noise2 = mkNoise2 noise2Base {-# INLINE noise2 #-}  noise2Base :: (RealFrac a) => Seed -> a -> a -> a noise2Base seed xo yo =-  let f2 = 0.5 * (sqrt3 - 1)-      to = (xo + yo) * f2-      x = xo + to-      y = yo + to+  let !f2 = 0.5 * (sqrt3 - 1)+      !to = (xo + yo) * f2+      !x = xo + to+      !y = yo + to -      fx = floor x-      fy = floor y-      xi = x - fromIntegral fx-      yi = y - fromIntegral fy+      !fx = floor x+      !fy = floor y+      !xi = x - fromIntegral fx+      !yi = y - fromIntegral fy -      t = (xi + yi) * g2-      x0 = xi - t-      y0 = yi - t-      i = fx * primeX-      j = fy * primeY+      !t = (xi + yi) * g2+      !x0 = xi - t+      !y0 = yi - t+      !i = fx * primeX+      !j = fy * primeY -      a = 0.5 - x0 * x0 - y0 * y0-      n0-        | a <= 0 = 0-        | otherwise =-            (a * a)-              * (a * a)-              * gradCoord2 seed i j x0 y0+      !a = 0.5 - x0 * x0 - y0 * y0+      n0 = attenuate a seed i j x0 y0 -      n1-        | y0 > x0 =-            let ~x1 = x0 + g2-                ~i1 = i-                ~y1 = y0 + (g2 - 1)-                ~j1 = j + primeY-                ~b = 0.5 - x1 * x1 - y1 * y1-             in if b <= 0-                  then 0-                  else-                    (b * b)-                      * (b * b)-                      * gradCoord2 seed i1 j1 x1 y1-        | otherwise =-            let ~x1 = x0 + (g2 - 1)-                ~i1 = i + primeX-                ~y1 = y0 + g2-                ~j1 = j-                ~b = 0.5 - x1 * x1 - y1 * y1-             in if b <= 0-                  then 0-                  else-                    (b * b)-                      * (b * b)-                      * gradCoord2 seed i1 j1 x1 y1+      n1 =+        let gt = y0 > x0+            -- Select the constant-folded addend per branch (g2 or g2 - 1),+            -- reproducing FNL's `x0 + (float)G2` / `x0 + ((float)G2 - 1)`+            -- rounding. Arithmetic on the selector, e.g.+            -- (x0 + g2 - 1) + cond, rounds differently when |x0 + g2| < 1.+            x1 = x0 + bool (g2 - 1) g2 gt+            y1 = y0 + bool g2 (g2 - 1) gt+            i1 = i + bool primeX 0 gt+            j1 = j + bool 0 primeY gt+            b = 0.5 - x1 * x1 - y1 * y1+         in attenuate b seed i1 j1 x1 y1 -      c =+      !n2 =         let g2t = 1 - 2 * g2-         in 2 * g2t * (1 / g2 - 2) * t-              + (-2 * g2t * g2t + a)-      n2-        | c <= 0 = 0-        | otherwise =-            let ~x2 = x0 + (2 * g2 - 1)-                ~y2 = y0 + (2 * g2 - 1)-             in (c * c)-                  * (c * c)-                  * gradCoord2 seed (i + primeX) (j + primeY) x2 y2-   in (n0 + n1 + n2) * 99.83685446303647-{-# INLINE noise2Base #-}+            c = 2 * g2t * (1 / g2 - 2) * t + (-2 * g2t * g2t + a)+            x2 = x0 + (2 * g2 - 1)+            y2 = y0 + (2 * g2 - 1)+         in attenuate c seed (i + primeX) (j + primeY) x2 y2+   in normalize $ n0 + n1 + n2+{-# INLINE [2] noise2Base #-}++attenuate :: (RealFrac a) => a -> Seed -> Hash -> Hash -> a -> a -> a+attenuate !vi seed i j x y =+  let !v = max 0 vi+   in (v * v) * (v * v) * gradCoord2 seed i j x y+{-# INLINE attenuate #-}++normalize :: (RealFrac a) => a -> a+normalize = (99.83685446303647 *)+{-# INLINE normalize #-}++noise3 :: (RealFrac a) => Noise3 a+noise3 = mkNoise3 noise3Base+{-# INLINE noise3 #-}++noise3Base :: forall a. (RealFrac a) => Seed -> a -> a -> a -> a+noise3Base seed0 xo yo zo =+  let !(x, y, z) = rotate3 xo yo zo++      !i0 = fastRound x+      !j0 = fastRound y+      !k0 = fastRound z+      !x0 = x - fromIntegral i0+      !y0 = y - fromIntegral j0+      !z0 = z - fromIntegral k0++      -- FNL: (int)(-1.0f - x0) | 1, i.e. -1 when the offset is >= 0+      !xns = bool 1 (-1) (x0 >= 0) :: Hash+      !yns = bool 1 (-1) (y0 >= 0) :: Hash+      !zns = bool 1 (-1) (z0 >= 0) :: Hash++      !ax0 = fromIntegral xns * negate x0+      !ay0 = fromIntegral yns * negate y0+      !az0 = fromIntegral zns * negate z0++      !ip = i0 * primeX+      !jp = j0 * primeY+      !kp = k0 * primeZ++      !a0 = (0.6 - x0 * x0) - (y0 * y0 + z0 * z0)++      !v0 = iteration seed0 a0 ip jp kp x0 y0 z0 ax0 ay0 az0 xns yns zns++      -- second lattice: reflect offsets, flip signs, complement the seed+      !ax1 = 0.5 - ax0+      !ay1 = 0.5 - ay0+      !az1 = 0.5 - az0+      !x1 = fromIntegral xns * ax1+      !y1 = fromIntegral yns * ay1+      !z1 = fromIntegral zns * az1+      !a1 = a0 + ((0.75 - ax1) - (ay1 + az1))+      !ip' = ip + ((xns `shiftR` 1) .&. primeX)+      !jp' = jp + ((yns `shiftR` 1) .&. primeY)+      !kp' = kp + ((zns `shiftR` 1) .&. primeZ)++      !v1 = iteration (complement seed0) a1 ip' jp' kp' x1 y1 z1 ax1 ay1 az1 (negate xns) (negate yns) (negate zns)+   in (v0 + v1) * 32.69428253173828125+ where+  -- one loop iteration of the FNL reference: the cell contribution plus one+  -- step along the dominant axis+  iteration+    :: Seed -> a -> Hash -> Hash -> Hash -> a -> a -> a -> a -> a -> a -> Hash -> Hash -> Hash -> a+  iteration !sd !a !i !j !k !x0 !y0 !z0 !ax !ay !az !xns !yns !zns =+    let !va+          | a > 0 = (a * a) * (a * a) * gradCoord3 sd i j k x0 y0 z0+          | otherwise = 0+        !b0 = a + 1+        !vb+          | ax >= ay && ax >= az =+              let !x1 = x0 + fromIntegral xns+                  !b = b0 - fromIntegral (xns * 2) * x1+               in bContrib sd b (i - xns * primeX) j k x1 y0 z0+          | ay > ax && ay >= az =+              let !y1 = y0 + fromIntegral yns+                  !b = b0 - fromIntegral (yns * 2) * y1+               in bContrib sd b i (j - yns * primeY) k x0 y1 z0+          | otherwise =+              let !z1 = z0 + fromIntegral zns+                  !b = b0 - fromIntegral (zns * 2) * z1+               in bContrib sd b i j (k - zns * primeZ) x0 y0 z1+     in va + vb+  {-# INLINE iteration #-}++  bContrib :: Seed -> a -> Hash -> Hash -> Hash -> a -> a -> a -> a+  bContrib !sd !b !i !j !k !x1 !y1 !z1+    | b > 0 = (b * b) * (b * b) * gradCoord3 sd i j k x1 y1 z1+    | otherwise = 0+  {-# INLINE bContrib #-}+{-# INLINE [2] noise3Base #-}
src/Numeric/Noise/Perlin.hs view
@@ -1,5 +1,3 @@-{-# LANGUAGE Strict #-}- -- | -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com> -- Stability : experimental@@ -18,7 +16,7 @@ import Numeric.Noise.Internal.Math  noise2 :: (RealFrac a) => Noise2 a-noise2 = Noise2 noise2Base+noise2 = mkNoise2 noise2Base {-# INLINE noise2 #-}  noise2Base :: forall a. (RealFrac a) => Seed -> a -> a -> a@@ -39,8 +37,8 @@        x1p = x0p + primeX       y1p = y0p + primeY-   in 1.4247691104677813-        * lerp+   in normalize2 $+        lerp           ( lerp               (gradCoord2 seed x0p y0p xd0 yd0)               (gradCoord2 seed x1p y0p xd1 yd0)@@ -52,10 +50,14 @@               u           )           v-{-# INLINE noise2Base #-}+{-# INLINE [2] noise2Base #-} +normalize2 :: (RealFrac a) => a -> a+normalize2 = (1.4247691104677813 *)+{-# INLINE normalize2 #-}+ noise3 :: (RealFrac a) => Noise3 a-noise3 = Noise3 noise3Base+noise3 = mkNoise3 noise3Base {-# INLINE noise3 #-}  noise3Base :: (RealFrac a) => Seed -> a -> a -> a -> a@@ -82,8 +84,8 @@       x1p = x0p + primeX       y1p = y0p + primeY       z1p = z0p + primeZ-   in 0.96492141485214233398437-        * lerp+   in normalize3 $+        lerp           ( lerp               ( lerp                   (gradCoord3 seed x0p y0p z0p xd0 yd0 zd0)@@ -111,4 +113,8 @@               v           )           w-{-# INLINE noise3Base #-}+{-# INLINE [2] noise3Base #-}++normalize3 :: (RealFrac a) => a -> a+normalize3 = (0.96492141485214233398437 *)+{-# INLINE normalize3 #-}
src/Numeric/Noise/SuperSimplex.hs view
@@ -4,20 +4,26 @@ -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com> -- Stability: experimental ----- This module implements a variation of OpenSimplex2 noise derived from FastNoiseLite.--- See openSimplex2S+-- This module implements a variation of OpenSimplex2S noise derived from+-- FastNoiseLite, exported from "Numeric.Noise" as 'Numeric.Noise.superSimplex2'+-- and 'Numeric.Noise.superSimplex3'. module Numeric.Noise.SuperSimplex (   -- * 2D Noise   noise2,   noise2Base,++  -- * 3D Noise+  noise3,+  noise3Base, ) where  import Data.Bits+import Data.Bool (bool) import Numeric.Noise.Internal import Numeric.Noise.Internal.Math  noise2 :: (RealFrac a) => Noise2 a-noise2 = Noise2 noise2Base+noise2 = mkNoise2 noise2Base {-# INLINE noise2 #-}  noise2Base :: (RealFrac a) => Seed -> a -> a -> a@@ -60,89 +66,225 @@             let ~x2 = x0 + (3 * g2 - 2)                 ~y2 = y0 + (3 * g2 - 1)                 ~a2 = (2 / 3) - x2 * x2 - y2 * y2-             in if a2 > 0-                  then-                    (a2 * a2)-                      * (a2 * a2)-                      * gradCoord2 seed (i + (primeX `shiftL` 1)) (j + primeY) x2 y2-                  else 0+             in attenuate a2 seed (i + (primeX `shiftL` 1)) (j + primeY) x2 y2         | otherwise =             let ~x2 = x0 + g2                 ~y2 = y0 + (g2 - 1)                 ~a2 = (2 / 3) - x2 * x2 - y2 * y2-             in if a2 > 0-                  then-                    (a2 * a2)-                      * (a2 * a2)-                      * gradCoord2 seed i (j + primeY) x2 y2-                  else 0+             in attenuate a2 seed i (j + primeY) x2 y2+       ~vgy         | yi - xmyi > 1 =             let ~x3 = x0 + (3 * g2 - 1)                 ~y3 = y0 + (3 * g2 - 2)                 ~a3 = (2 / 3) - x3 * x3 - y3 * y3-             in if a3 > 0-                  then-                    (a3 * a3)-                      * (a3 * a3)-                      * gradCoord2 seed (i + primeX) (j + (primeY `shiftL` 1)) x3 y3-                  else 0+             in attenuate a3 seed (i + primeX) (j + (primeY `shiftL` 1)) x3 y3         | otherwise =             let ~x3 = x0 + (g2 - 1)                 ~y3 = y0 + g2                 ~a3 = (2 / 3) - x3 * x3 - y3 * y3-             in if a3 > 0-                  then-                    (a3 * a3)-                      * (a3 * a3)-                      * gradCoord2 seed (i + primeX) j x3 y3-                  else 0+             in attenuate a3 seed (i + primeX) j x3 y3        ~vlx         | xi + xmyi < 0 =             let ~x2 = x0 + (1 - g2)                 ~y2 = y0 - g2                 ~a2 = (2 / 3) - x2 * x2 - y2 * y2-             in if a2 > 0-                  then-                    (a2 * a2)-                      * (a2 * a2)-                      * gradCoord2 seed (i - primeX) j x2 y2-                  else 0+             in attenuate a2 seed (i - primeX) j x2 y2         | otherwise =             let ~x2 = x0 + (g2 - 1)                 ~y2 = y0 + g2                 ~a2 = (2 / 3) - x2 * x2 - y2 * y2-             in if a2 > 0-                  then-                    (a2 * a2)-                      * (a2 * a2)-                      * gradCoord2 seed (i + primeX) j x2 y2-                  else 0+             in attenuate a2 seed (i + primeX) j x2 y2       ~vly         | yi < xmyi =             let ~x2 = x0 - g2                 ~y2 = y0 - (g2 - 1)                 ~a2 = (2 / 3) - x2 * x2 - y2 * y2-             in if a2 > 0-                  then-                    (a2 * a2)-                      * (a2 * a2)-                      * gradCoord2 seed i (j - primeY) x2 y2-                  else 0+             in attenuate a2 seed i (j - primeY) x2 y2         | otherwise =             let ~x2 = x0 + g2                 ~y2 = y0 + (g2 - 1)                 ~a2 = (2 / 3) - x2 * x2 - y2 * y2-             in if a2 > 0-                  then-                    (a2 * a2)-                      * (a2 * a2)-                      * gradCoord2 seed i (j + primeY) x2 y2-                  else 0+             in attenuate a2 seed i (j + primeY) x2 y2        v2         | t > g2 = vgx + vgy         | otherwise = vlx + vly-   in (v0 + v1 + v2) * 18.24196194486065-{-# INLINE noise2Base #-}+   in normalize $ v0 + v1 + v2+{-# INLINE [2] noise2Base #-}++attenuate :: (RealFrac a) => a -> Seed -> Hash -> Hash -> a -> a -> a+attenuate !vi !seed !i !j !x !y =+  let !v = max 0 vi+   in (v * v) * (v * v) * gradCoord2 seed i j x y+{-# INLINE attenuate #-}++normalize :: (RealFrac a) => a -> a+normalize = (18.24196194486065 *)+{-# INLINE normalize #-}++noise3 :: (RealFrac a) => Noise3 a+noise3 = mkNoise3 noise3Base+{-# INLINE noise3 #-}++noise3Base :: (RealFrac a) => Seed -> a -> a -> a -> a+noise3Base seed xo yo zo =+  let (x, y, z) = rotate3 xo yo zo++      fi = floor x :: Hash+      fj = floor y :: Hash+      fk = floor z :: Hash+      xi = x - fromIntegral fi+      yi = y - fromIntegral fj+      zi = z - fromIntegral fk++      i = fi * primeX+      j = fj * primeY+      k = fk * primeZ+      seed2 = seed + 1293373++      -- FNL: (int)(-0.5f - xi), i.e. -1 when the offset is >= 0.5, else 0+      xnm = bool 0 (-1) (xi >= 0.5) :: Hash+      ynm = bool 0 (-1) (yi >= 0.5) :: Hash+      znm = bool 0 (-1) (zi >= 0.5) :: Hash++      x0 = xi + fromIntegral xnm+      y0 = yi + fromIntegral ynm+      z0 = zi + fromIntegral znm+      a0 = 0.75 - x0 * x0 - y0 * y0 - z0 * z0+      v0 =+        q a0+          * gradCoord3 seed (i + (xnm .&. primeX)) (j + (ynm .&. primeY)) (k + (znm .&. primeZ)) x0 y0 z0++      x1 = xi - 0.5+      y1 = yi - 0.5+      z1 = zi - 0.5+      a1 = 0.75 - x1 * x1 - y1 * y1 - z1 * z1+      v1 = q a1 * gradCoord3 seed2 (i + primeX) (j + primeY) (k + primeZ) x1 y1 z1++      xFlip0 = fromIntegral ((xnm .|. 1) `shiftL` 1) * x1+      yFlip0 = fromIntegral ((ynm .|. 1) `shiftL` 1) * y1+      zFlip0 = fromIntegral ((znm .|. 1) `shiftL` 1) * z1+      xFlip1 = fromIntegral (-2 - (xnm `shiftL` 2)) * x1 - 1.0+      yFlip1 = fromIntegral (-2 - (ynm `shiftL` 2)) * y1 - 1.0+      zFlip1 = fromIntegral (-2 - (znm `shiftL` 2)) * z1 - 1.0++      a2 = xFlip0 + a0+      ~(vX, skip5)+        | a2 > 0 =+            let ~x2 = x0 - fromIntegral (xnm .|. 1)+             in ( q a2+                    * gradCoord3 seed (i + (complement xnm .&. primeX)) (j + (ynm .&. primeY)) (k + (znm .&. primeZ)) x2 y0 z0+                , False+                )+        | otherwise =+            let a3 = yFlip0 + zFlip0 + a0+                ~v3+                  | a3 > 0 =+                      let ~y3 = y0 - fromIntegral (ynm .|. 1)+                          ~z3 = z0 - fromIntegral (znm .|. 1)+                       in q a3+                            * gradCoord3 seed (i + (xnm .&. primeX)) (j + (complement ynm .&. primeY)) (k + (complement znm .&. primeZ)) x0 y3 z3+                  | otherwise = 0+                a4 = xFlip1 + a1+                ~(v4, sk)+                  | a4 > 0 =+                      let ~x4 = fromIntegral (xnm .|. 1) + x1+                       in ( q a4+                              * gradCoord3 seed2 (i + (xnm .&. (primeX * 2))) (j + primeY) (k + primeZ) x4 y1 z1+                          , True+                          )+                  | otherwise = (0, False)+             in (v3 + v4, sk)++      a6 = yFlip0 + a0+      ~(vY, skip9)+        | a6 > 0 =+            let ~y6 = y0 - fromIntegral (ynm .|. 1)+             in ( q a6+                    * gradCoord3 seed (i + (xnm .&. primeX)) (j + (complement ynm .&. primeY)) (k + (znm .&. primeZ)) x0 y6 z0+                , False+                )+        | otherwise =+            let a7 = xFlip0 + zFlip0 + a0+                ~v7+                  | a7 > 0 =+                      let ~x7 = x0 - fromIntegral (xnm .|. 1)+                          ~z7 = z0 - fromIntegral (znm .|. 1)+                       in q a7+                            * gradCoord3 seed (i + (complement xnm .&. primeX)) (j + (ynm .&. primeY)) (k + (complement znm .&. primeZ)) x7 y0 z7+                  | otherwise = 0+                a8 = yFlip1 + a1+                ~(v8, sk)+                  | a8 > 0 =+                      let ~y8 = fromIntegral (ynm .|. 1) + y1+                       in ( q a8+                              * gradCoord3 seed2 (i + primeX) (j + (ynm .&. (primeY `shiftL` 1))) (k + primeZ) x1 y8 z1+                          , True+                          )+                  | otherwise = (0, False)+             in (v7 + v8, sk)++      aA = zFlip0 + a0+      ~(vZ, skipD)+        | aA > 0 =+            let ~zA = z0 - fromIntegral (znm .|. 1)+             in ( q aA+                    * gradCoord3 seed (i + (xnm .&. primeX)) (j + (ynm .&. primeY)) (k + (complement znm .&. primeZ)) x0 y0 zA+                , False+                )+        | otherwise =+            let aB = xFlip0 + yFlip0 + a0+                ~vB+                  | aB > 0 =+                      let ~xB = x0 - fromIntegral (xnm .|. 1)+                          ~yB = y0 - fromIntegral (ynm .|. 1)+                       in q aB+                            * gradCoord3 seed (i + (complement xnm .&. primeX)) (j + (complement ynm .&. primeY)) (k + (znm .&. primeZ)) xB yB z0+                  | otherwise = 0+                aC = zFlip1 + a1+                ~(vC, sk)+                  | aC > 0 =+                      let ~zC = fromIntegral (znm .|. 1) + z1+                       in ( q aC+                              * gradCoord3 seed2 (i + primeX) (j + primeY) (k + (znm .&. (primeZ `shiftL` 1))) x1 y1 zC+                          , True+                          )+                  | otherwise = (0, False)+             in (vB + vC, sk)++      ~v5+        | not skip5+        , a5 <- yFlip1 + zFlip1 + a1+        , a5 > 0 =+            let ~y5 = fromIntegral (ynm .|. 1) + y1+                ~z5 = fromIntegral (znm .|. 1) + z1+             in q a5+                  * gradCoord3 seed2 (i + primeX) (j + (ynm .&. (primeY `shiftL` 1))) (k + (znm .&. (primeZ `shiftL` 1))) x1 y5 z5+        | otherwise = 0++      ~v9+        | not skip9+        , a9 <- xFlip1 + zFlip1 + a1+        , a9 > 0 =+            let ~x9 = fromIntegral (xnm .|. 1) + x1+                ~z9 = fromIntegral (znm .|. 1) + z1+             in q a9+                  * gradCoord3 seed2 (i + (xnm .&. (primeX * 2))) (j + primeY) (k + (znm .&. (primeZ `shiftL` 1))) x9 y1 z9+        | otherwise = 0++      ~vD+        | not skipD+        , aD <- xFlip1 + yFlip1 + a1+        , aD > 0 =+            let ~xD = fromIntegral (xnm .|. 1) + x1+                ~yD = fromIntegral (ynm .|. 1) + y1+             in q aD+                  * gradCoord3 seed2 (i + (xnm .&. (primeX `shiftL` 1))) (j + (ynm .&. (primeY `shiftL` 1))) (k + primeZ) xD yD z1+        | otherwise = 0+   in (v0 + v1 + vX + vY + vZ + v5 + v9 + vD) * 9.046026385208288+ where+  q a = (a * a) * (a * a)+  {-# INLINE q #-}+{-# INLINE [2] noise3Base #-}
src/Numeric/Noise/Value.hs view
@@ -1,5 +1,3 @@-{-# LANGUAGE Strict #-}- -- | -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com> -- Stability: experimental@@ -20,7 +18,7 @@ import Numeric.Noise.Internal.Math  noise2 :: (RealFrac a) => Noise2 a-noise2 = Noise2 noise2Base+noise2 = mkNoise2 noise2Base {-# INLINE noise2 #-}  noise2Base :: (RealFrac a) => Seed -> a -> a -> a@@ -48,10 +46,10 @@             xs         )         ys-{-# INLINE noise2Base #-}+{-# INLINE [2] noise2Base #-}  noise3 :: (RealFrac a) => Noise3 a-noise3 = Noise3 noise3Base+noise3 = mkNoise3 noise3Base {-# INLINE noise3 #-}  noise3Base :: (RealFrac a) => Seed -> a -> a -> a -> a@@ -99,4 +97,4 @@             ys         )         zs-{-# INLINE noise3Base #-}+{-# INLINE [2] noise3Base #-}
src/Numeric/Noise/ValueCubic.hs view
@@ -1,5 +1,3 @@-{-# LANGUAGE Strict #-}- -- | -- Maintainer: Jeremy Nuttall <jeremy@jeremy-nuttall.com> -- Stability : experimental@@ -18,7 +16,7 @@ import Numeric.Noise.Internal.Math  noise2 :: (RealFrac a) => Noise2 a-noise2 = Noise2 noise2Base+noise2 = mkNoise2 noise2Base {-# INLINE noise2 #-}  noise2Base :: (RealFrac a) => Seed -> a -> a -> a@@ -68,10 +66,10 @@               xs           )           ys-{-# INLINE noise2Base #-}+{-# INLINE [2] noise2Base #-}  noise3 :: (RealFrac a) => Noise3 a-noise3 = Noise3 noise3Base+noise3 = mkNoise3 noise3Base {-# INLINE noise3 #-}  noise3Base :: (RealFrac a) => Seed -> a -> a -> a -> a@@ -223,4 +221,4 @@               ys           )           zs-{-# INLINE noise3Base #-}+{-# INLINE [2] noise3Base #-}
+ test/CellularSpec.hs view
@@ -0,0 +1,67 @@+{-# LANGUAGE OverloadedStrings #-}++module CellularSpec (test_golden_cellular) where++import Golden.Util+import Numeric.Noise+import Test.Tasty (TestTree, testGroup)++test_golden_cellular :: TestTree+test_golden_cellular =+  testGroup+    "Cellular Golden Tests"+    [ testGroup "Grid Tests" cellularGridTests+    , testGroup "Sparse Tests" cellularSparseTests+    , testGroup "3D Grid Tests" cellular3DGridTests+    , testGroup "3D Sparse Tests" cellular3DSparseTests+    ]++-- All combinations of distance functions and result types+allCellularConfigs :: [(CellularDistanceFn, CellularResult)]+allCellularConfigs = [(df, rt) | df <- [minBound .. maxBound], rt <- [minBound .. maxBound]]++cellularGridTests :: [TestTree]+cellularGridTests =+  [ goldenImageTest2D "cellular" variant (cellular2 config) seed+  | (distFn, result) <- allCellularConfigs+  , let config = defaultCellularConfig{cellularDistanceFn = distFn, cellularResult = result}+  , seed <- cellularSeeds+  , let variant = show distFn ++ "-" <> show result <> "-seed" ++ show seed+  ]++cellularSparseTests :: [TestTree]+cellularSparseTests =+  [ goldenSparseTest2D "cellular" variant (cellular2 config) seed+  | (distFn, result) <- allCellularConfigs+  , let config = defaultCellularConfig{cellularDistanceFn = distFn, cellularResult = result}+  , seed <- cellularSeeds+  , let variant = show distFn <> "-" <> show result <> "-seed" ++ show seed+  ]++-- Full 3D image goldens would add ~200 PNGs; sparse JSON covers the whole+-- config matrix, images sample one distance function across result shapes.+cellular3DImageConfigs :: [(CellularDistanceFn, CellularResult)]+cellular3DImageConfigs =+  [ (DistEuclidean, CellValue)+  , (DistEuclidean, Distance)+  , (DistEuclidean, Distance2Add)+  ]++cellular3DGridTests :: [TestTree]+cellular3DGridTests =+  [ goldenImageTest3D "cellular" variant (cellular3 config) seed zOffset+  | (distFn, result) <- cellular3DImageConfigs+  , let config = defaultCellularConfig{cellularDistanceFn = distFn, cellularResult = result}+  , seed <- cellularSeeds+  , (idx, zOffset) <- zip [0 :: Int ..] sliceOffsets3D+  , let variant = "3d-" <> show distFn <> "-" <> show result <> "-seed_" <> show seed <> "-slice_" <> show idx+  ]++cellular3DSparseTests :: [TestTree]+cellular3DSparseTests =+  [ goldenSparseTest3D "cellular" variant (cellular3 config) seed+  | (distFn, result) <- allCellularConfigs+  , let config = defaultCellularConfig{cellularDistanceFn = distFn, cellularResult = result}+  , seed <- cellularSeeds+  , let variant = "3d-" <> show distFn <> "-" <> show result <> "-seed" <> show seed+  ]
+ test/FractalSpec.hs view
@@ -0,0 +1,68 @@+{-# LANGUAGE OverloadedStrings #-}++module FractalSpec (test_golden_fractal) where++import Golden.Util+import Numeric.Noise+import Test.Tasty (TestTree, testGroup)++test_golden_fractal :: TestTree+test_golden_fractal =+  testGroup+    "Fractal Golden Tests"+    [ testGroup "2D Grid Tests" fractal2DGridTests+    , testGroup "2D Sparse Tests" fractal2DSparseTests+    , testGroup "3D Grid Tests" fractal3DGridTests+    , testGroup "3D Sparse Tests" fractal3DSparseTests+    ]++-- Fractal types to test+data FractalType = FBM | Billow | Ridged | PingPong+  deriving (Show, Eq, Enum, Bounded)++-- Apply the fractal type to a 2D noise function+applyFractal2D :: FractalType -> Noise2 Double -> Noise2 Double+applyFractal2D FBM = fractal2 defaultFractalConfig+applyFractal2D Billow = billow2 defaultFractalConfig+applyFractal2D Ridged = ridged2 defaultFractalConfig+applyFractal2D PingPong = pingPong2 defaultFractalConfig defaultPingPongStrength++-- Apply the fractal type to a 3D noise function+applyFractal3D :: FractalType -> Noise3 Double -> Noise3 Double+applyFractal3D FBM = fractal3 defaultFractalConfig+applyFractal3D Billow = billow3 defaultFractalConfig+applyFractal3D Ridged = ridged3 defaultFractalConfig+applyFractal3D PingPong = pingPong3 defaultFractalConfig defaultPingPongStrength++fractal2DGridTests :: [TestTree]+fractal2DGridTests =+  [ goldenImageTest2D "fractal" variant (applyFractal2D fractalType perlin2) seed+  | fractalType <- [minBound .. maxBound]+  , seed <- cellularSeeds+  , let variant = show fractalType ++ "-perlin-2d-seed" ++ show seed+  ]++fractal2DSparseTests :: [TestTree]+fractal2DSparseTests =+  [ goldenSparseTest2D "fractal" variant (applyFractal2D fractalType perlin2) seed+  | fractalType <- [minBound .. maxBound]+  , seed <- cellularSeeds+  , let variant = show fractalType ++ "-perlin-2d-seed" ++ show seed+  ]++fractal3DGridTests :: [TestTree]+fractal3DGridTests =+  [ goldenImageTest3D "fractal" variant (applyFractal3D fractalType perlin3) seed zOffset+  | fractalType <- [minBound .. maxBound]+  , seed <- cellularSeeds+  , (idx, zOffset) <- zip [0 :: Int ..] sliceOffsets3D+  , let variant = show fractalType ++ "-perlin-3d-seed_" ++ show seed ++ "-slice_" ++ show idx+  ]++fractal3DSparseTests :: [TestTree]+fractal3DSparseTests =+  [ goldenSparseTest3D "fractal" variant (applyFractal3D fractalType perlin3) seed+  | fractalType <- [minBound .. maxBound]+  , seed <- cellularSeeds+  , let variant = show fractalType ++ "-perlin-3d-seed" ++ show seed+  ]
+ test/Golden/Util.hs view
@@ -0,0 +1,387 @@+{-# LANGUAGE OverloadedStrings #-}++-- | Utilities for golden testing of noise functions+module Golden.Util (+  -- * Test configuration+  defaultSeeds,+  cellularSeeds,+  sliceOffsets3D,++  -- * Grid generation+  generateGrid2D,+  generateGrid3D,++  -- * Sparse sampling+  SparseTest (..),+  generateSparse2D,+  generateSparse3D,++  -- * High-level test builders+  goldenImageTest2D,+  goldenImageTest3D,+  goldenSparseTest2D,+  goldenSparseTest3D,++  -- * Convenience batch functions+  golden2DImageTests,+  golden2DSparseTests,+  golden3DImageTests,+  golden3DSparseTests,+) where++import Codec.Picture+import Control.Monad+import Data.Aeson (FromJSON, ToJSON)+import Data.Aeson.Encode.Pretty (encodePretty)+import Data.ByteString qualified as BS+import Data.ByteString.Lazy qualified as LB+import Data.Massiv.Array (Array, B (..), Comp (..), Ix2 (..), Ix3, IxN (..), Sz (..))+import Data.Massiv.Array qualified as M+import Data.Text.Lazy qualified as LT+import Data.Text.Lazy.Encoding qualified as LT+import Foreign.C (eNOENT)+import Foreign.C.Error (errnoToIOError)+import GHC.Generics (Generic)+import Numeric.Noise (Noise2, Noise3, Seed, noise2At, noise3At, sliceZ3)+import System.Directory+import System.Exit+import System.FilePath+import System.Process.Typed qualified as PT+import Test.Tasty (TestName, TestTree, askOption)+import Test.Tasty.Golden+import Test.Tasty.Golden.Advanced (goldenTest2)++defaultSeeds :: [Seed]+defaultSeeds = [0, 42, 12345]++cellularSeeds :: [Seed]+cellularSeeds = [0, 42]++width2D, height2D :: Int+width2D = 1024+height2D = 1024++width3D, height3D :: Int+width3D = 256+height3D = 256++-- | Z-offsets for 3D slicing (fractional positions avoiding edges)+sliceOffsets3D :: [Double]+sliceOffsets3D = [0.125, 0.375, 0.625, 0.875]++data SparseTest a = SparseTest+  { coordinates :: [a]+  , expected :: a+  }+  deriving (Eq, Show, Generic)++instance (FromJSON a) => FromJSON (SparseTest a)+instance (ToJSON a) => ToJSON (SparseTest a)++-- | Generate a 2D noise grid using massiv+generateGrid2D+  :: Noise2 Double+  -> Seed+  -> Int+  -- ^ Width+  -> Int+  -- ^ Height+  -> Array B Ix2 Double+generateGrid2D noise seed width height =+  M.makeArray Par (Sz2 height width) $ \(row :. col) ->+    let x = fromIntegral col / fromIntegral width+        y = fromIntegral row / fromIntegral height+     in noise2At noise seed x y+{-# INLINE generateGrid2D #-}++-- | Generate a 3D noise grid using massiv+generateGrid3D+  :: Noise3 Double+  -> Seed+  -> Int+  -- ^ Width+  -> Int+  -- ^ Height+  -> Int+  -- ^ Depth+  -> Array B Ix3 Double+generateGrid3D noise seed width height depth =+  M.makeArray Par (Sz3 depth height width) $ \(d :> row :. col) ->+    let x = fromIntegral col / fromIntegral width+        y = fromIntegral row / fromIntegral height+        z = fromIntegral d / fromIntegral depth+     in noise3At noise seed x y z+{-# INLINE generateGrid3D #-}++-- | Convert a 2D noise grid to a grayscale PNG image+-- Maps noise values from [-1, 1] to pixel values [0, 255]+noiseGridToImage :: Array B Ix2 Double -> Image Pixel8+noiseGridToImage arr =+  let Sz2 height width = M.size arr+      getPixel x y =+        let val = arr M.! (y :. x)+            -- Map [-1, 1] to [0, 255]+            normalized = (val + 1.0) / 2.0+            clamped = max 0.0 (min 1.0 normalized)+         in round (clamped * 255.0)+   in generateImage getPixel width height+{-# INLINE noiseGridToImage #-}++-- | Strategic test points for 2D noise+-- Includes corners, edges, zero, unit values, negatives, and fractional coordinates+sparseTestPoints2D :: [(Double, Double)]+sparseTestPoints2D =+  [ -- Corners and edges+    (0.0, 0.0)+  , (1.0, 1.0)+  , (0.0, 1.0)+  , (1.0, 0.0)+  , -- Negative values+    (-1.0, -1.0)+  , (-1.0, 0.0)+  , (0.0, -1.0)+  , (-1.0, 1.0)+  , (1.0, -1.0)+  , -- Fractional coordinates+    (0.5, 0.5)+  , (0.25, 0.75)+  , (0.75, 0.25)+  , (0.1, 0.9)+  , (0.9, 0.1)+  , -- Larger values+    (10.0, 10.0)+  , (100.0, 100.0)+  , (-10.0, -10.0)+  , (5.5, 7.3)+  , (-3.2, 4.7)+  , -- Edge cases+    (1.0e-10, 1.0e-10)+  , -- More varied points+    (2.5, 3.7)+  , (-5.2, 8.9)+  , (12.34, -56.78)+  , (0.123, 0.456)+  , (0.789, 0.321)+  , (-0.5, -0.5)+  , (0.5, -0.5)+  , (-0.5, 0.5)+  , -- Prime-like coordinates for good distribution+    (2.0, 3.0)+  , (5.0, 7.0)+  , (11.0, 13.0)+  , (17.0, 19.0)+  , (23.0, 29.0)+  , (31.0, 37.0)+  , (41.0, 43.0)+  , (47.0, 53.0)+  , -- Diagonal patterns+    (2.0, 2.0)+  , (3.0, 3.0)+  , (-2.0, -2.0)+  , -- Anti-diagonal+    (2.0, -2.0)+  , (-2.0, 2.0)+  , -- Discontinuity+    (0.999999, 0.999999)+  , (0.000001, 0.000001)+  , (0.999999999, 0.999999999)+  , (1.000000001, 1.000000001)+  , -- Powers of two+    (256.0, 256.0)+  , (1024.0, 1024.1)+  , (65536.5, 65536.5)+  , -- Large inputs+    (10000.0, 10000.0)+  , (10000.1, 10000.1)+  ]++-- | Strategic test points for 3D noise+sparseTestPoints3D :: [(Double, Double, Double)]+sparseTestPoints3D =+  [ -- Corners+    (0.0, 0.0, 0.0)+  , (1.0, 1.0, 1.0)+  , (0.0, 0.0, 1.0)+  , (0.0, 1.0, 0.0)+  , (1.0, 0.0, 0.0)+  , (0.0, 1.0, 1.0)+  , (1.0, 0.0, 1.0)+  , (1.0, 1.0, 0.0)+  , -- Negative corners+    (-1.0, -1.0, -1.0)+  , (-1.0, -1.0, 1.0)+  , (-1.0, 1.0, -1.0)+  , (1.0, -1.0, -1.0)+  , -- Fractional center and edges+    (0.5, 0.5, 0.5)+  , (0.25, 0.5, 0.75)+  , (0.75, 0.25, 0.5)+  , -- Larger values+    (10.0, 10.0, 10.0)+  , (100.0, 100.0, 100.0)+  , (-10.0, -10.0, -10.0)+  , -- Varied points+    (2.5, 3.7, 4.2)+  , (-5.2, 8.9, -3.1)+  , (1.23, -4.56, 7.89)+  , -- Edge cases+    (1.0e-10, 1.0e-10, 1.0e-10)+  , -- Mixed signs+    (1.0, -1.0, 1.0)+  , (-1.0, 1.0, -1.0)+  , (1.0, 1.0, -1.0)+  , (-1.0, -1.0, 1.0)+  , -- Prime-like distribution+    (2.0, 3.0, 5.0)+  , (7.0, 11.0, 13.0)+  , (17.0, 19.0, 23.0)+  ]++-- | Generate sparse test samples for 2D noise+generateSparse2D :: Noise2 Double -> Seed -> [SparseTest Double]+generateSparse2D noise seed =+  map (\(x, y) -> SparseTest [x, y] (noise2At noise seed x y)) sparseTestPoints2D++-- | Generate sparse test samples for 3D noise+generateSparse3D :: Noise3 Double -> Seed -> [SparseTest Double]+generateSparse3D noise seed =+  map (\(x, y, z) -> SparseTest [x, y, z] (noise3At noise seed x y z)) sparseTestPoints3D++-- -----------------------------------------------------------------------------+-- High-level test builders+-- -----------------------------------------------------------------------------++goldenDir :: FilePath+goldenDir = "test-data" </> "golden"++goldenImageTest :: String -> String -> (String -> IO ()) -> TestTree+goldenImageTest noiseName variant act =+  let testName = noiseName <> " " <> variant+      imageRoot = goldenDir </> "images" </> noiseName+      goldenPath = imageRoot </> variant <.> "png"+      actualPath = imageRoot </> variant <.> "actual" <.> "png"+   in goldenVsImage+        testName+        goldenPath+        actualPath+        (createDirectoryIfMissing True imageRoot >> act actualPath)++-- This is more-or-less the same as goldenVsFileDiff, but it doesn't share stdio with+-- the child process, which is pretty important because odiff doesn't have a quiet option+goldenVsImage :: TestName -> FilePath -> FilePath -> IO () -> TestTree+goldenVsImage name ref new act = askOption $ \sizeCutoff ->+  goldenTest2+    name+    throwIfDoesNotExist+    act+    (\_ _ -> runDiff sizeCutoff)+    update+    delete+ where+  throwIfDoesNotExist = do+    exists <- doesFileExist ref+    unless exists $+      ioError $+        errnoToIOError "goldenVsFileDiff" eNOENT Nothing Nothing+  runDiff+    :: SizeCutoff+    -> IO (Maybe String)+  runDiff sizeCutoff = do+    let (refName, refExt) = splitExtension ref+        proc =+          PT.proc+            "odiff"+            [ "-t"+            , "0.004" -- Tolerate roughly +/- 1 error for 8-bit grayscale.+            , "--diff-overlay"+            , "--fail-on-layout"+            , "--output-diff-lines"+            , ref+            , new+            , refName <.> "diff" <.> refExt+            ]+        procConf = PT.setStdin PT.closed proc++    (exitCode, out) <- PT.readProcessInterleaved procConf+    return $ case exitCode of+      ExitSuccess -> Nothing+      _ -> Just . LT.unpack . LT.decodeUtf8 . truncateLargeOutput sizeCutoff $ out+  truncateLargeOutput (SizeCutoff n) str =+    if LB.length str <= n+      then str+      else+        LB.take n str+          <> "<truncated>"+          <> "\nUse --accept or increase --size-cutoff to see full output."+  update _ = do+    f <- BS.readFile new+    createDirectoriesAndWriteFile ref (LB.fromStrict f)+  delete = removeFile new++goldenImageTest2D :: String -> String -> Noise2 Double -> Seed -> TestTree+goldenImageTest2D noiseName variant noise seed = goldenImageTest noiseName variant $ \path -> do+  let grid = generateGrid2D noise seed width2D height2D+      img = noiseGridToImage grid+  savePngImage path (ImageY8 img)++goldenImageTest3D :: String -> String -> Noise3 Double -> Seed -> Double -> TestTree+goldenImageTest3D noiseName variant noise seed zOffset = goldenImageTest noiseName variant $ \path -> do+  let grid2D = generateGrid2D (sliceZ3 zOffset noise) seed width3D height3D+      img = noiseGridToImage grid2D+  savePngImage path (ImageY8 img)++goldenSparseTest :: String -> String -> (String -> IO ()) -> TestTree+goldenSparseTest noiseName variant act =+  let testName = noiseName <> " " <> variant <> " (sparse)"+      jsonRoot = goldenDir </> "sparse" </> noiseName+      goldenPath = jsonRoot </> variant <.> "json"+      actualPath = jsonRoot </> variant <.> "actual" <.> "json"+   in goldenVsFileDiff+        testName+        (\ref new -> ["diff", "-u", ref, new])+        goldenPath+        actualPath+        (createDirectoryIfMissing True jsonRoot >> act actualPath)++goldenSparseTest2D :: String -> String -> Noise2 Double -> Seed -> TestTree+goldenSparseTest2D noiseName variant noise seed = goldenSparseTest noiseName variant $ \path -> do+  let samples = generateSparse2D noise seed+      json = encodePretty samples+  LB.writeFile path json++goldenSparseTest3D :: String -> String -> Noise3 Double -> Seed -> TestTree+goldenSparseTest3D noiseName variant noise seed = goldenSparseTest noiseName variant $ \path -> do+  let samples = generateSparse3D noise seed+      json = encodePretty samples+  LB.writeFile path json++labelBatch :: (Show a) => String -> a -> String+labelBatch dim seed = dim <> "-seed_" <> show seed++labelBatch3D :: Seed -> Int -> String+labelBatch3D seed sliceIdx = "3d-seed_" <> show seed <> "-slice_" <> show sliceIdx++golden2DImageTests :: String -> [Seed] -> Noise2 Double -> [TestTree]+golden2DImageTests noiseName seeds noise =+  [ goldenImageTest2D noiseName (labelBatch "2d" seed) noise seed+  | seed <- seeds+  ]++golden2DSparseTests :: String -> [Seed] -> Noise2 Double -> [TestTree]+golden2DSparseTests noiseName seeds noise =+  [ goldenSparseTest2D noiseName (labelBatch "2d" seed) noise seed+  | seed <- seeds+  ]++golden3DImageTests :: String -> [Seed] -> Noise3 Double -> [TestTree]+golden3DImageTests noiseName seeds noise =+  [ goldenImageTest3D noiseName (labelBatch3D seed idx) noise seed zOffset+  | seed <- seeds+  , (idx, zOffset) <- zip [0 ..] sliceOffsets3D+  ]++golden3DSparseTests :: String -> [Seed] -> Noise3 Double -> [TestTree]+golden3DSparseTests noiseName seeds noise =+  [ goldenSparseTest3D noiseName (labelBatch "3d" seed) noise seed+  | seed <- seeds+  ]
test/Noise2Spec.hs view
@@ -1,7 +1,6 @@ module Noise2Spec where  import Numeric.Noise-import Numeric.Noise.Internal  seed :: Seed seed = 55@@ -25,12 +24,12 @@ prop_0_is_additive_identity :: Rational -> Rational -> Rational -> Bool prop_0_is_additive_identity v x y =   let n1 = const2 v-   in noise2At (n1 + fromInteger 0) seed x y == noise2At n1 seed x y+   in noise2At (n1 + 0) seed x y == noise2At n1 seed x y  prop_negate_is_additive_inverse :: Rational -> Rational -> Rational -> Bool prop_negate_is_additive_inverse v x y =   let n1 = const2 v-   in noise2At (n1 + negate n1) seed x y == 0+   in noise2At (n1 - n1) seed x y == 0  prop_multiplication :: Rational -> Rational -> Bool prop_multiplication x y = noise2At (const2 x * const2 y) seed x y == x * y@@ -41,8 +40,3 @@       n2 = const2 2027       n3 = const2 2069    in noise2At ((n1 * n2) * n3) seed x y == noise2At (n1 * (n2 * n3)) seed x y--prop_1_is_multiplicative_identity :: Rational -> Rational -> Rational -> Bool-prop_1_is_multiplicative_identity v x y =-  let n1 = const2 v-   in noise2At (n1 * fromInteger 1) seed x y == v
test/Noise3Spec.hs view
@@ -1,7 +1,6 @@ module Noise3Spec where  import Numeric.Noise-import Numeric.Noise.Internal  seed :: Seed seed = 2381@@ -26,12 +25,12 @@ prop_0_is_additive_identity :: Rational -> Rational -> Rational -> Rational -> Bool prop_0_is_additive_identity v x y z =   let n1 = const3 v-   in noise3At (n1 + fromInteger 0) seed x y z == noise3At n1 seed x y z+   in noise3At (n1 + 0) seed x y z == noise3At n1 seed x y z  prop_negate_is_additive_inverse :: Rational -> Rational -> Rational -> Rational -> Bool prop_negate_is_additive_inverse v x y z =   let n1 = const3 v-   in noise3At (n1 + negate n1) seed x y z == 0+   in noise3At (n1 - n1) seed x y z == 0  prop_multiplication :: Rational -> Rational -> Rational -> Bool prop_multiplication x y z =@@ -47,4 +46,4 @@ prop_1_is_multiplicative_identity :: Rational -> Rational -> Rational -> Rational -> Bool prop_1_is_multiplicative_identity v x y z =   let n1 = const3 v-   in noise3At (n1 * fromInteger 1) seed x y z == v+   in noise3At (n1 * 1) seed x y z == v
+ test/OpenSimplexSpec.hs view
@@ -0,0 +1,29 @@+{-# LANGUAGE OverloadedStrings #-}++module OpenSimplexSpec (test_golden_opensimplex) where++import Golden.Util+import Numeric.Noise+import Test.Tasty (TestTree, testGroup)++test_golden_opensimplex :: TestTree+test_golden_opensimplex =+  testGroup+    "OpenSimplex Golden Tests"+    [ testGroup "2D Grid Tests" openSimplex2DGridTests+    , testGroup "2D Sparse Tests" openSimplex2DSparseTests+    , testGroup "3D Grid Tests" openSimplex3DGridTests+    , testGroup "3D Sparse Tests" openSimplex3DSparseTests+    ]++openSimplex2DGridTests :: [TestTree]+openSimplex2DGridTests = golden2DImageTests "opensimplex" defaultSeeds openSimplex2++openSimplex2DSparseTests :: [TestTree]+openSimplex2DSparseTests = golden2DSparseTests "opensimplex" defaultSeeds openSimplex2++openSimplex3DGridTests :: [TestTree]+openSimplex3DGridTests = golden3DImageTests "opensimplex" defaultSeeds openSimplex3++openSimplex3DSparseTests :: [TestTree]+openSimplex3DSparseTests = golden3DSparseTests "opensimplex" defaultSeeds openSimplex3
test/PerlinSpec.hs view
@@ -1,6 +1,9 @@ module PerlinSpec where +import GHC.Exts (noinline)+import Golden.Util import Numeric.Noise+import Test.Tasty (TestTree, testGroup)  seed :: Seed seed = 82384@@ -12,8 +15,32 @@  prop_noise2_addition_associative :: Rational -> Rational -> Bool prop_noise2_addition_associative x y =-  noise2At ((perlin2 + perlin2) + perlin2) seed x y == noise2At (perlin2 + (perlin2 + perlin2)) seed x y+  noise2At ((noinline perlin2 + noinline superSimplex2) + noinline openSimplex2) seed x y+    == noise2At (perlin2 + (noinline superSimplex2 + noinline openSimplex2)) seed x y  prop_noise2_addition_commutative :: Rational -> Rational -> Bool prop_noise2_addition_commutative x y =-  noise2At (perlin2 + perlin2) seed x y == noise2At (perlin2 + perlin2) seed x y+  noise2At (noinline perlin2 + noinline superSimplex2) seed x y+    == noise2At (noinline superSimplex2 + noinline perlin2) seed x y++test_golden_perlin :: TestTree+test_golden_perlin =+  testGroup+    "Perlin Golden Tests"+    [ testGroup "2D Grid Tests" perlin2DGridTests+    , testGroup "2D Sparse Tests" perlin2DSparseTests+    , testGroup "3D Grid Tests" perlin3DGridTests+    , testGroup "3D Sparse Tests" perlin3DSparseTests+    ]++perlin2DGridTests :: [TestTree]+perlin2DGridTests = golden2DImageTests "perlin" defaultSeeds perlin2++perlin2DSparseTests :: [TestTree]+perlin2DSparseTests = golden2DSparseTests "perlin" defaultSeeds perlin2++perlin3DGridTests :: [TestTree]+perlin3DGridTests = golden3DImageTests "perlin" defaultSeeds perlin3++perlin3DSparseTests :: [TestTree]+perlin3DSparseTests = golden3DSparseTests "perlin" defaultSeeds perlin3
+ test/SuperSimplexSpec.hs view
@@ -0,0 +1,27 @@+module SuperSimplexSpec (test_golden_supersimplex) where++import Golden.Util+import Numeric.Noise+import Test.Tasty (TestTree, testGroup)++test_golden_supersimplex :: TestTree+test_golden_supersimplex =+  testGroup+    "SuperSimplex Golden Tests"+    [ testGroup "2D Grid Tests" superSimplex2DGridTests+    , testGroup "2D Sparse Tests" superSimplex2DSparseTests+    , testGroup "3D Grid Tests" superSimplex3DGridTests+    , testGroup "3D Sparse Tests" superSimplex3DSparseTests+    ]++superSimplex2DGridTests :: [TestTree]+superSimplex2DGridTests = golden2DImageTests "supersimplex" defaultSeeds superSimplex2++superSimplex2DSparseTests :: [TestTree]+superSimplex2DSparseTests = golden2DSparseTests "supersimplex" defaultSeeds superSimplex2++superSimplex3DGridTests :: [TestTree]+superSimplex3DGridTests = golden3DImageTests "supersimplex" defaultSeeds superSimplex3++superSimplex3DSparseTests :: [TestTree]+superSimplex3DSparseTests = golden3DSparseTests "supersimplex" defaultSeeds superSimplex3
+ test/TotalitySpec.hs view
@@ -0,0 +1,60 @@+-- | Out-of-domain inputs (beyond the Int32 lattice, non-finite) produce+-- unspecified /values/, but they must stay values: every noise function is+-- total, so one bad coordinate upstream can't crash a whole render. These+-- assertions replace the old out-of-domain golden points, which pinned the+-- exact garbage and so broke on any implementation change.+module TotalitySpec (test_totality) where++import Control.Exception (evaluate)+import Control.Monad (forM_, void)+import Numeric.Noise+import Test.Tasty (TestTree, testGroup)+import Test.Tasty.HUnit (testCase)++-- Beyond the Int32 lattice, past Double integer precision, and non-finite.+badCoords :: [Double]+badCoords = [1.0e10, -1.0e10, 2 ^ (53 :: Int), 1 / 0, -1 / 0, 0 / 0]++noises2 :: [(String, Noise2 Double)]+noises2 =+  [ ("perlin2", perlin2)+  , ("openSimplex2", openSimplex2)+  , ("superSimplex2", superSimplex2)+  , ("value2", value2)+  , ("valueCubic2", valueCubic2)+  , ("cellular2", cellular2 defaultCellularConfig)+  , ("fractal2 perlin2", fractal2 defaultFractalConfig perlin2)+  ]++noises3 :: [(String, Noise3 Double)]+noises3 =+  [ ("perlin3", perlin3)+  , ("openSimplex3", openSimplex3)+  , ("superSimplex3", superSimplex3)+  , ("value3", value3)+  , ("valueCubic3", valueCubic3)+  , ("cellular3", cellular3 defaultCellularConfig)+  , ("fractal3 perlin3", fractal3 defaultFractalConfig perlin3)+  ]++test_totality :: TestTree+test_totality =+  testGroup+    "Totality on out-of-domain inputs"+    [ testGroup+        "2D"+        [ testCase name $+            forM_ badCoords $ \c ->+              forM_ [(c, 0.5), (0.5, c), (c, c)] $ \(x, y) ->+                void $ evaluate (noise2At noise 0 x y)+        | (name, noise) <- noises2+        ]+    , testGroup+        "3D"+        [ testCase name $+            forM_ badCoords $ \c ->+              forM_ [(c, 0.5, 0.5), (0.5, c, 0.5), (0.5, 0.5, c), (c, c, c)] $ \(x, y, z) ->+                void $ evaluate (noise3At noise 0 x y z)+        | (name, noise) <- noises3+        ]+    ]
+ test/ValueCubicSpec.hs view
@@ -0,0 +1,27 @@+module ValueCubicSpec (test_golden_valuecubic) where++import Golden.Util+import Numeric.Noise+import Test.Tasty (TestTree, testGroup)++test_golden_valuecubic :: TestTree+test_golden_valuecubic =+  testGroup+    "ValueCubic Golden Tests"+    [ testGroup "2D Grid Tests" valueCubic2DGridTests+    , testGroup "2D Sparse Tests" valueCubic2DSparseTests+    , testGroup "3D Grid Tests" valueCubic3DGridTests+    , testGroup "3D Sparse Tests" valueCubic3DSparseTests+    ]++valueCubic2DGridTests :: [TestTree]+valueCubic2DGridTests = golden2DImageTests "valuecubic" defaultSeeds valueCubic2++valueCubic2DSparseTests :: [TestTree]+valueCubic2DSparseTests = golden2DSparseTests "valuecubic" defaultSeeds valueCubic2++valueCubic3DGridTests :: [TestTree]+valueCubic3DGridTests = golden3DImageTests "valuecubic" defaultSeeds valueCubic3++valueCubic3DSparseTests :: [TestTree]+valueCubic3DSparseTests = golden3DSparseTests "valuecubic" defaultSeeds valueCubic3
+ test/ValueSpec.hs view
@@ -0,0 +1,29 @@+{-# LANGUAGE OverloadedStrings #-}++module ValueSpec (test_golden_value) where++import Golden.Util+import Numeric.Noise+import Test.Tasty (TestTree, testGroup)++test_golden_value :: TestTree+test_golden_value =+  testGroup+    "Value Golden Tests"+    [ testGroup "2D Grid Tests" value2DGridTests+    , testGroup "2D Sparse Tests" value2DSparseTests+    , testGroup "3D Grid Tests" value3DGridTests+    , testGroup "3D Sparse Tests" value3DSparseTests+    ]++value2DGridTests :: [TestTree]+value2DGridTests = golden2DImageTests "value" defaultSeeds value2++value2DSparseTests :: [TestTree]+value2DSparseTests = golden2DSparseTests "value" defaultSeeds value2++value3DGridTests :: [TestTree]+value3DGridTests = golden3DImageTests "value" defaultSeeds value3++value3DSparseTests :: [TestTree]+value3DSparseTests = golden3DSparseTests "value" defaultSeeds value3